POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell'Informazione

Corso di Laurea Magistrale in

Ingegneria Meccanica

Mechanical device to support the flexion-

extension of the elbow in post-stroke spasticity

Relator: Prof. Hermes Giberti

Co-relator: Eng. Matteo Malosio

Thesis of:

Giulio Flavio Luigi

Francesco Schifino

Matr. 824160

Academic year 2015 – 2016

iii

Contents

Abstract ....................................................................................................................... 1

Chapter 1 Introduction ................................................................................................. 3

Overview of the issues related to upper limb rehabilitation ............................ 3

Specific problems concerning the elbow joint in hypotonic patients .............. 7

State of art ....................................................................................................... 8

Chapter 2 Device description .................................................................................... 15

Design specifications ..................................................................................... 15

General operation of the device ..................................................................... 16

Hooking, releasing and charging mechanisms .............................................. 19

Mechanism regulation ................................................................................... 28

Transmission and regulation of the torsional spring ..................................... 32

Device components list ................................................................................. 32

Chapter 3 Device sizing ............................................................................................ 35

Genera sizing ................................................................................................. 35

Sizing of the setting mechanism .................................................................... 39

Transmissions design .................................................................................... 43

FEM analysis of the most stressed components ............................................ 50

Dynamic simulation with rigid bodies model ............................................... 62

iv

Chapter 4 Prototype realization ................................................................................ 69

Specification of the prototype ....................................................................... 69

Parts produced with CNC ............................................................................. 70

Parts produced with 3D printer ..................................................................... 71

Chapter 5 Conclusion and future developments ....................................................... 73

Bibliography ............................................................................................................. 75

v

Figure Index

Figure 1.1 LIGHTarm exoskeleton CAD .............................................................. 5

Figure 1.2 Human arm kinematic scheme and range of motion of the joints

without and with the LIGHTarm exoskeleton .............................................. 6

Figure 1.3 LIGHTarm exoskeleton kinematic scheme and joints range of motion

....................................................................................................................... 6

Figure 1.4 Human arm kinematic scheme and joints range of motion ................. 8

Figure 1.5 Automatic watch with a transparent case back, showing its eccentric

weight ............................................................................................................ 9

Figure 1.6 Magneti Marelli Kinetic energy recovery system ............................. 10

Figure 1.7 NASA Flywheel energy storage ........................................................ 11

Figure 1.8 JAS EZ elbow Orthosis ..................................................................... 12

Figure 1.9 Retractable pen mechanism ............................................................... 13

Figure 2.1 Device view with highlighted the spring-arm in yellow and the exo-

arm in orange ............................................................................................... 17

Figure 2.2 Scheme of the extension movement of the elbow with highlighted in

green the discharging zone .......................................................................... 18

Figure 2.3 Scheme of the flexion movement of the elbow with highlighted in

blue the charging zone ................................................................................ 18

Figure 2.4 View of the spring-arm with highlighted in blue the support, in red

the charging-block and in green the sledge ................................................. 20

Figure 2.5 Explosion view of the sledge ............................................................. 20

Figure 2.6 Two views of the Exo-arm with highlighted in red the superior ramp

and in blue the inferior ramp ....................................................................... 21

Figure 2.7 Schematic representation of the beginning of the hooking phase 1: the

ramp of the exo-arm (orange) enters in contact with the superior shaft of

the sledge (yellow) ...................................................................................... 22

Figure 2.8 Schematic representation of the beginning of the hooking phase 2: the

inferior shaft (yellow) starts to climb the step of the support disc (red) by

itself ............................................................................................................. 22

Figure 2.9 Schematic representation of the end of the hooking phase 2: the ramp

of the sledge (yellow) enters in contact with the inferior ramp of the exo-

arm (orange) ................................................................................................ 23

Figure 2.10 Schematic representation of the start of the releasing phase: the

inferior shaft of the sledge (yellow) comes to the ramp of the support disc

(red) ............................................................................................................. 23

Figure 2.11 Schematic representation of the releasing phase: The sledge

(yellow) starts to go down following the ramp of the support disc (red) .... 24

Figure 2.12 Schematic representation of the releasing phase: The sledge

(yellow) completed the descendent and the exo-arm (orange) is free to

come back .................................................................................................... 24

vi

Figure 2.13 View of the recharging-block with highlighted in blue the contact

plate............................................................................................................. 25

Figure 2.14 Schematic representation of the charging phase: Finished the phase

of discharge the exo-arm (orange) is free to move and comes back during

the flexion movement ................................................................................. 26

Figure 2.15 Schematic representation of the charging phase: The exo-arm

(orange) enters in contact with contact plate (blue).................................... 26

Figure 2.16 Schematic representation of the charging phase: The exo-arm

(orange) pushes the contact plate (blue) so the sledge (yellow) goes up the

ramp of the support disc (red) and goes forward the hooking point ........... 27

Figure 2.17 Schematic representation of the charging phase: The sledge (yellow)

comes in proximity of the step of the support disc (red) ............................ 27

Figure 2.18 Schematic representation of the charging phase: The sledge falls

down in the hooking point of the support disc (red) pushed by the contrast

spring .......................................................................................................... 27

Figure 2.19 View of the releasing compartment: Extreme position in extension

.................................................................................................................... 29

Figure 2.20 View of the releasing compartment: Extreme position in flexion .. 29

Figure 2.21 View of the hooking compartment: Position of minimum extension

.................................................................................................................... 30

Figure 2.22 View of the hooking sector: Position of maximum extension ........ 30

Figure 2.23 View of the charging compartment: In blue the charging-block .... 31

Figure 3.1 Example of circular ramp, prospected view on left and lateral view on

right ............................................................................................................. 36

Figure 3.2 View of spring-arm with highlighted in red the sides of the

articulated parallelogram ............................................................................ 38

Figure 3.3 Scheme for the calculation of the horizontal movement of the sledge

.................................................................................................................... 39

Figure 3.4 View of the setting mechanism for the range of discharge with

highlighted in red the articulated quadrilateral ........................................... 40

Figure 3.5 Scheme 1 for the design of the setting mechanism for the discharging

range ........................................................................................................... 41

Figure 3.6 Scheme 2 for the design of the setting mechanism for the discharging

range ........................................................................................................... 42

Figure 3.7 View of the gear transmission of the device, in grey the bull gear and

in orange the pinion .................................................................................... 44

Figure 3.8 Schematic representation of the torque spring transmission, in grey

the torque spring, in yellow the Spring-arm shaft and in red the wire who

connects the previous elements .................................................................. 46

Figure 3.9 Graphic of the length l in function of the angle α ............................. 47

Figure 3.10 Graphic of the angle β in function of the angle α ............................ 48

Figure 3.11 Graphic of the ratio r in function of the angle α .............................. 49

vii

Figure 3.12 FEM analysis of the inferior shaft first design, Von Mises Stress

arrangement ................................................................................................. 52

Figure 3.13 FEM analysis of the inferior shaft first design, Displacement

arrangement ................................................................................................. 52

Figure 3.14 FEM analysis of the inferior shaft first design, Safety Factor

arrangement ................................................................................................. 53

Figure 3.15 FEM analysis of the inferior shaft final design, Von Mises Stress

arrangement ................................................................................................. 54

Figure 3.16 FEM analysis of the inferior shaft final design, displacement

arrangement ................................................................................................. 54

Figure 3.17 FEM analysis of the inferior shaft final design, Safety Factor

arrangement ................................................................................................. 55

Figure 3.18 FEM analysis of the exo-arm superior ramp, Von Mises Stress

arrangement ................................................................................................. 56

Figure 3.19 FEM analysis of the Exo-arm superior ramp, displacement

arrangement ................................................................................................. 57

Figure 3.20 FEM analysis of the Exo-arm superior ramp, Safety Factor

arrangement ................................................................................................. 57

Figure 3.21 FEM analysis of the Exo-arm inferior ramp, Von Mises Stress

arrangement ................................................................................................. 58

Figure 3.22 FEM analysis of the Exo-arm inferior ramp, displacement

arrangement ................................................................................................. 59

Figure 3.23 FEM analysis of the Exo-arm inferior ramp, Safety Factor

arrangement ................................................................................................. 59

Figure 3.24 FEM analysis of the sledge ramp, Von Mises Stress arrangement .. 60

Figure 3.25 FEM analysis of the sledge ramp, displacement arrangement ........ 61

Figure 3.26 FEM analysis of the sledge ramp, Safety Factor arrangement ........ 61

Figure 3.27 View of the simplified model of the device used for the dynamic

simulation .................................................................................................... 62

Figure 3.28 View of the simplified model in order to see the contact between the

sledge inferior shaft and the Hooking-block in the simulation start point .. 63

Figure 3.29 Graphic of the theoretical working cycle of the device in function of

the flexion angle .......................................................................................... 65

Figure 3.30 Dynamic Simulation results: Torque transmitted to the user during

the discharging phase .................................................................................. 66

Figure 3.31 Dynamic Simulation results: Sledge elevation during the

discharging phase ........................................................................................ 67

Figure 3.32 Dynamic Simulation results: Torque transmitted in function of the

sledge elevation ........................................................................................... 68

Figure 4.1 Front view of the prototype ............................................................... 70

Figure 4.2 Rear view of the prototype ................................................................ 70

Figure 5.1 View of the device mounted on the LIGHTarm exoskeleton ............ 73

viii

Abstract

The purpose of this dissertation is to present an innovative device for upper limb

rehabilitation and, in particular, for the flexion-extension of the elbow for patients

struggling with the complete extension of the joint. The device has been designed

for LIGHT arm, the exoskeleton for rehabilitation developed by the Institute of

Industrial Technology and Automation part of the Italian National Research

Council. Its primary function is to provide a driving torque to support the

extension of the elbow in a range near the complete extension of the joint. The

energy needed for this aid is provided by the patient himself during the flexion

movement, limited to the area of complete flexion, where the patient usually

presents enough residual muscular tone. A torsional spring is used as energy

accumulator and, furthermore, the device does not require any forms of power

beyond the energy transmitted by the patient.

Index terms – Exoskeleton, rehabilitation, spring mechanism, snap mechanism,

elbow flexion-extension, torsional spring.

2

Chapter 1

Introduction

Overview of the issues related to upper limb rehabilitation

The upper limb provides a significant contribution to the implementation of daily

activates (Activities of Daily Living, ADL); state this, any type of impairment that

reduce the mobility of the limb will negatively affect the quality of life. Issues to

the upper limb maybe caused by deficit or damage to the musculoskeletal system

or the central nervous system. The most common clinic condition concerning

resulting after these events id the spasticity. There are several definition of

spasticity, but the one that seems to be the more widely accepted is the one of

Lance (1980) [1]:

“Spasticity is a motor disorder characterized by a velocity

dependent increase in tonic stretch reflexes (muscle tone) with

exaggerated tendon jerks, resulting from hyper-excitability of

the stretch reflexes, as one component of the upper

motoneuron syndrome”

First, following the definition, we can infer that the spasticity is identified with

“muscle hypertonicity” – if we try to move a paretic limb, we will encounter more

resistance the more is the speed at which we make the movement; second, the

definition implies that this is a condition affecting the muscles that the patient is

unable to control, since, with the damage, the brain lost the possibility to adjust

the movement in any way.

Recently Lance’s definition has been considered too strict and it has been

expanded:

“Sensory-disordered motor control, resulting from an upper

motorneuron injury, which comes as involuntary activation of

the muscles in an intermittent or continuous way”

Now spasticity means both a generic neuromotor issue – a disorder that arises

from neurological problems – and a condition that damage the performance of the

musculoskeletal system. Stated this, the spasticity causes may be:

- Infantile cerebral paralysis – persistent but non-progressive disorder of

posture and movement, due to alterations of cerebral function before the

central nervous system has completed its development;

- Stroke – pathological cerebral vascular event, resulting in acute

disturbance of brain function, focal or generalized;

Chapter 1

4

- Multiple sclerosis – chronic autoimmune demyelinating disease that

affects nerve cells making difficult the communication between the brain

and spinal cord;

- Head injuries – It occurs when an external force traumatically injures the

brain. They are the leading cause of disability worldwide;

- Spinal injuries – Injuries that may result from the interruption of the

ascending and descending nerve pathways of the spinal cord. They may

be a consequence of a trauma, of a tumor process or of ischemia and

determine a paralysis of the lower limbs and, in severe cases, even higher

ones;

- Anoxia – Pathological condition resulting in the cells suffering due to lack

of oxygen.

Scope of the rehabilitation is to involve the patient in evolving his competencies

by:

- Exploiting the remaining functional systems;

- Developing new ability to better achieve the control of himself and the

surroundings;

- Reducing the unwell perception caused by the limitation imposed by the

biological damage.

Summarizing, the function of the neurological rehabilitation is to help the recover,

at least partial, of the lost functionalities in order to allow the patient to realize the

movement typical of ADL.

The phenomenon known as Neuroplasticity is what allows this functional recover.

Neuroplasticity refers to the fact that the Control Neural System (CNS) is able to

experience structural and functional changes in response to physiological events,

environmental stimuli (ex. learning), and pathological events. Therefore, in

patients with lesions affecting the CNS, neuroplasticity represents a mechanisms

of spontaneous recovery and, if properly interpreted, can serve as rational basis to

promote targeted rehabilitative approaches.

Furthermore, recent studies have shown that training after injury can revive neural

plasticity and functional recovery in the limb [2]. The human brain is not only

sensitive to the experience, but is able to retain this plasticity after injuries

Without going into further details, we can say that the brain has the ability to

compensate brain injuries with specific mechanisms and neuroplasticity is the

biological substrate that allows the recovery considering the physiological

conditions (for more detail [3]).

Introduction

5

Concerning the rehabilitation

The exoskeleton LIGHTarm developed by the Institute of Industrial Technology

and Automation (ITIA) – which is part of the National Research Council (CNR)

– is, in its version not implemented, an exoskeleton for the rehabilitation of upper

limb. This device provides an antigravity support to the patient's arm, allowing

patients with a muscle hypotonus to perform movements in almost all the volume

of work. Its particular shape allows a good handling of the limb and, in particular,

implements various ingenious solutions thanks to the connection between the

robotic arm to the human one at the shoulder and elbow level. More details on

this can be found in the articles [4], [5], [6], [7], [8], [9], [10].

Figure 1.1 LIGHTarm exoskeleton CAD

Chapter 1

6

Figure 1.2 Human arm kinematic scheme and range of motion of the joints

without and with the LIGHTarm exoskeleton

Figure 1.3 LIGHTarm exoskeleton kinematic scheme and joints range of motion

Introduction

7

Specific problems concerning the elbow joint in hypotonic

patients

A characteristic of spasticity, which should be emphasized in this specific context,

is that the muscle tone depends on the speed of the movement, that is, it increases

with the increase of the speed of movement. It causes the so-called “Switchblade

effect” in the passive limb movements involving both the agonist and the

antagonists muscles, thus interfering with both extension and bending of the body

part [11].

In order to better understand the function of the proposed device, it is worth

emphasize that spasticity is always accompanied by a disturbance in muscle

strength and, in particular, it affects more the antigravity muscles; the practical

effect is that, in the upper limbs, we can find a predominance of the flexion spasms

(and so the flexor muscles), while in the lower limbs the spasm of extensors

prevails. This pathophysiology is the starting point to assess adequately a device

that stores energy during the muscle flexion of the limb, and then gives it in the

extension, when the muscle of the patient experiences a strength deficit.

Stated this, after some analysis done on post stroke patients, it has been shown

that in patients with muscular hypotonus there are more pronounced difficulties

in elbow extension, especially in the area close to full extension, although it is

still maintained a higher muscle tone in the flexion. For these reasons, the patient

was able to exert maximum force in the area close to the full flexion of the arm.

These analysis has made clear the need to implement a kinematic joint in the

design of the LIGHTarm exoskeleton placed at the elbow, in order to support the

elbow extension phase in the patients.

Looking at the kinematic scheme of the exoskeleton (figure1.3), we see that the

elbow joint is associated with two rotational degrees of freedom (𝐮e,1 and 𝐮e,2)

oriented perpendicularly. These form a universal joint centered in the intersection

of the two axes of rotation (Oee) in which the patient’s elbow should be located

(as shown by the figure (1.3)).

Then, a stage of preliminary study showed that the vast majority of rehabilitation

exercises for this kind of diseases are carried out keeping the flexion-extension of

the elbow at a horizontal level; then, observing the figure (1.2), the axis of rotation

(𝐮h,4) will be angled of a few degrees with respect to the 𝑥 axis of the main

reference gaming system (ground). Following this, it was decided to seek a

solution to implement by involving only the last joint.

Chapter 1

8

Figure 1.4 Human arm kinematic scheme and joints range of motion

It arises then the idea to design a mechanical device that implements the rotation

(𝐉𝒆,𝟐), in order to provide an aid to the patient in the extension of the elbow when

the axis of rotation is next to the vertical one.

State of art

The fundamental concept of the device is to accumulate energy in a certain range

of motion and then release it in a different range. There are several devices that

use the same concept for similar purposes, from the charging mechanism of

watches up to the most modern KERS (Kinetic Energy Recovery System) used in

Formula 1. The kinetic energy can be stored and maintained in different ways, as

potential energy in a spring, converted into electrical energy and then stored in a

battery as chemical, or maintained as kinetic energy using rotating disks with very

low friction bearings in a vacuum environment.

Introduction

9

We can quickly examine a few examples:

Figure 1.5 Automatic watch with a transparent case back, showing its eccentric

weight

Self-winding watch – An automatic watch is a mechanical wrist watch which has

the characteristic of recharging itself by exploiting the movement of a rotor placed

in it. The rotor movement is caused by the movement of the surface on which it

is placed, like the arm of its owner, making unnecessary any operation of manual

winding. The rotor rotates around a pivot and, moving with the oscillation of the

arm, acts on the spring that charges the mechanism. In this case the energy

accumulator is a spiral spring [12].

Chapter 1

10

Figure 1.6 Magneti Marelli Kinetic energy recovery system

KERS by Magneti Marelli – Magneti Marelli has developed an innovative

technology for Formula 1 in the field of energy recovery. This system, called

KERS (Kinetic Energy Recovery System), is in fact a system that converts

mechanical energy into electrical energy to be stored in special batteries; the pilot,

then, may decide to re-use this energy in special conditions such as straights,

overtaking, or strategic points of the circuit.

The device is connected directly to the crankshaft through a motor-generator,

which, during braking, converts the kinetic energy into electric current. This

current, through the control unit and using shielded cabling, goes to recharge the

lithium-ion batteries. In acceleration, instead, when the pilot uses the boost, the

electrical energy is taken by the batteries and, always by means of the electronic

control unit, sent to the motor-generator that rotates in the reverse direction and

transmits the accelerating force on the motor shaft [13].

Introduction

11

Figure 1.7 NASA Flywheel energy storage

FES – The Flywheel Energy Storage (FES), is an electromechanical device

capable of energy storage in the form of rotational kinetic energy.

The basic idea is to accumulate energy by rapidly rotating a flywheel. This idea

is very interesting, since they can accumulate large amounts of energy in a "small"

object (with a good specific energy capacity) compared to other types of

accumulator, such as electrochemical cells [14].

None of these devices is used in rehabilitation; in fact, when speaking of

exoskeletons for the rehabilitation, electric motors are the most common solution

used to assist the movement of the elbow. The LIGHTarm exoskeletons, instead,

relieves the patient's arm from its weight, but still leaves to the patient the load of

the inertial contributions generated during the movement. However, there are

certain types of orthoses that, through a spring, exert over the limb contrasting

forces in order to make it move towards a given position following the therapy.

To cite one example:

Chapter 1

12

Figure 1.8 JAS EZ elbow Orthosis

JAS EZ Elbow – Stress relaxation and low-load stretch are established stretching

techniques that safely and efficiently restore normal length to shortened tissues

surrounding a joint, allowing for motion and use when stiffness develops after

injury. Stress relaxation and low-load stretch can be carried out by hand (via a

therapist) or by using JAS and JAS EZ product systems. During a stress relaxation

and low-load stretch therapy session, the joint is brought to a pain-free stretched

position and held there for several minutes, to allow for the surrounding tissues to

relax and lengthen. Once this occurs the joint is stretched and held again, and

more lengthening is achieved. This process is repeated several times to complete

a JAS treatment session [15].

Introduction

13

So, there are no exoskeletons hosting kinetic energy storage devices. All the

accumulation devices for kinetic energy considered have a differentiation

between accumulation stage and release stage that is exclusively temporal. What

we are introducing with the designed mechanism is the possibility to choose one

ROM (Range of Motion) for accumulating energy, one in which keep it

accumulated, and finally one in which release it. The aim is to keep these three

ranges within an angular sector of less than 360°. A common mechanism which

is probably the closest to the device developed is the retractable pen mechanism.

This mechanism, using a linear spring and specific geometrical constraints, allows

four a motion phases: the first in which the cartridge tip comes out, the second

which blocks the tip the reached position, the third which retract the tip of the

cartridge and then the last that locks it in the initial position.

Figure 1.9 Retractable pen mechanism

Chapter 1

14

Chapter 2

Device description

Design specifications

To be useful, the design of the mechanism should have the following

characteristics:

- Be small in size, so that it can be mounted directly on the exoskeleton. As already mentioned, the intention is to implement the last joint through

a small mechanism that can be easily installed or uninstalled on the arm.

Obviously it should not be too bulky, to not cause discomfort to the patient

during the movements, and it should not limit too much the range of

motion of the exoskeleton. So, the maximum overall dimensions that the

mechanism may have is defined by a cylinder of diameter 100 mm and

height of 20 mm centered on the selected joint.

- Do not use electricity. Not being electricity dependent allows the LIGHTarm to be installed

anywhere; to keep this characteristic the component will have to rely only

on the strength that the patient can give. The mechanism will act as simple

kinetic energy storage hosting the energy donated by the patient in the

favorable area, to be able to unleash it as an aid in the unfavorable one.

- Support the patient in the last phase of the elbow extension.

As we have already said, the ultimate purpose of the mechanism is to

provide energy with a supporting torque, which is added to the strength of

the patient; this in order to allow him to reach the full extension of the

elbow.

- Allow the patient to reload the mechanism in the area close to full

flexion.

The area in which the patient can afford to transfer energy to recharge the

mechanism is exactly the opposite end compared to where it needs to

receive it. The mechanism has to be able to keep the spring in position

while the patient's arm passes from one zone to another.

- Being as much adjustable as possible both in the width of the range of

action of the device and in the applied torque.

Chapter 2

16

The system needs to be adjustable based on the patient's needs. In fact, the

area in which each patient requires the aid of the device may vary widely

so, although the range of motion allowed by the exoskeleton for this type

of movement is 120 degrees, some patients may not be able to exploit it

all. The same issue can be found when speaking about the intensity of the

applied torque. It must therefore be able to being adjusted according to

individual needs.

- Keep the torque applied as much constant as possible. Once the necessary couple is chosen it should vary as little as possible. By

deciding to use a spring as an energy accumulator there may be the

problem that it could generate an inversely proportional torque against the

patient needs. In fact, in the zone of full extension the patient will require

the maximum torque but the spring will be near the point of minimum

torque that it can generate.

- Try to be as much gently as possible in order not to stress the arm

with excessive acceleration. A too rough trigger of the torque must be avoided since it may generate

yanks in the patient's arm.

- Once the extension is complete the patient should be able to freely

move the arm.

Except for the charging and recharging movement, the patient's arm

should not be influenced by the spring. So in the extension movement the

spring will intervene only close to the complete stretch, while in the

flexion only in the full close of the stretch. The rest of time the spring must

not be mechanically connected to the patient's arm.

General operation of the device

We now present the characteristics of the developed device and its general

operating operation, we will enter into the details of the technical solutions

implemented in the following paragraphs [21].

In its high-level operation scheme, the mechanism is based on two components

rotating around a common axis of rotation. One will have to move together with

the patient's arm and be rigidly connected to the last link of the exoskeleton, which

is in turn bound to the forearm of the patient. The second will be together with the

torsion spring with a shape that allows both the charging and the discharging.

These two components through different types of interaction between them in

different points of the work space will allow the coupling and uncoupling between

Device description

17

the exoskeleton’s arm – and consequently the patient arm – and the torsion spring.

Henceforth, we will call the component that moves together with the exoskeleton

exo-arm, while the other one connected with the spring, spring-arm.

In the following picture, the exo-arm in orange and the spring-arm in yellow.

Figure 2.1 Device view with highlighted the spring-arm in yellow and the exo-arm

in orange

We now analyze the work cycle of the device. Although the device is adjustable

both in the range of discharging and in the range of work, we set for clarity some

parameters that we are going to maintain constant from now on:

- Complete flexion 𝛼 = 0°. - Complete extension 𝛼 = 120°. - Charging zone 𝛼 = 0° ÷ 30°. - Discharging zone 𝛼 = 90° ÷ 120°. - Total working range 120°.

- Charging range 30°.

- Discharging range 30°.

Where 𝛼 is the independent coordinate representing the opening angle of the

patient's elbow.

A working cycle consist in four phases, two in which the patient’s arm interacts

with the spring (charge and discharge) and two in which the arm can move freely:

one after the complete flexion and one after the complete extension. Referring to

the figures (2.2) and (2.3), the cycle, starting from a complete flexion position,

takes place as follows:

Chapter 2

18

1. 𝜶 between 0° and 90°, Free Zone 1. The arm is free to move both in

extension and in flexion.

2. 𝜶 = 𝟗𝟎°, Hooking point. The arm comes into contact with the spring

which begins to pull in order to help the patient in the extension.

3. 𝜶 between 90° and 120°, Discharging Zone. Arm and spring are coupled

and the spring tends to extend the arm (green area).

4. 𝜶 = 𝟏𝟐𝟎°, Releasing Point. The spring leaves the arm free to move

again.

5. 𝜶 between 120° and 30°, Free Zone 2. Again the patient is free to move

without the contribution of the spring, neither in flexion nor in extension.

6. 𝜶 between 30° and 0° Charging Zone. The arm comes into contact with

the spring and by flexing the elbow the exo-arm charges the spring (blue

region). At complete flexion, the spring is fully recharged and the cycle

can start again.

Figure 2.2 Scheme of the extension movement of the elbow with highlighted in

green the discharging zone

Figure 2.3 Scheme of the flexion movement of the elbow with highlighted in

blue the charging zone

Device description

19

The hooking and releasing points are guaranteed by the particular geometry of the

support disk which, interacting with the spring-arm, allows this to hang in these

two specific points. For this reason, there are some fundamental conditions for the

cycle to function properly:

1. The arm must reach the release point to be able to be freed from the spring,

otherwise, the arms needs to return to the hooking point that also allows

the release. In this last case, however, the patient will have to work against

the spring.

2. The spring must be fully recharged in order to correctly complete the

cycle. If the complete charge is not reached, the spring will tend to

discharge again by returning to the releasing point.

Hooking, releasing and charging mechanisms

We now go more in detail regarding the interactions that take place among the

exo-arm, the spring-arm and the support disk in the hooking and releasing points.

Although so far we have spoken of the spring-arm as a single entity for simplicity

of exposition, it is composed of several pieces and it is in fact the more complex

subset of the device.

As the figure (2.4) shows, the spring-arm can be conceptually divided into three

parts:

- A support part connected to the torsion spring, to which are connected the

other parts (the blue parts).

- An adjustable part (by means of screws) used to charge the spring which

is nothing more than a small disc. This is bound to a flat surface, on which

the exo-arm acts pushing (red part).

- A part composed of an articulated parallelogram that allows the sledge to

move vertically (green part).

Chapter 2

20

Figure 2.4 View of the spring-arm with highlighted in blue the support, in red

the charging-block and in green the sledge

Focusing on the sledge, it has two side elements which support three components:

a superior shaft and a bar forming a circular ramp both interacting with the exo-

arm; a lower shaft that interacts with the support disc.

Figure 2.5 Explosion view of the sledge

Device description

21

Regarding the exo-arm, it has two circular ramps; one above and one below that

interact respectively with the superior shaft and with the ramp-bar.

Figure 2.6 Two views of the Exo-arm with highlighted in red the superior ramp

and in blue the inferior ramp

The support disc is designed to block the lower shaft with a vertical wall. A step,

with height equal to the lower shaft diameter, which blocks the spring-arm and

prevents the torsional spring to discharge. In order to overcome this step the

sledge will have to be raised by the exo-arm (note: the geometry of the

parallelogram coordinated with that of the support disk has been studied to

prevent the slide from rising alone). Once surmounted the step, the support disc

keeps the sledge at the same height until it reaches the release area in which,

through a ramp, it degrades to the initial level.

The hooking procedure can be divided into two phases:

- Phase 1. The superior ramp of the exo-arm comes into contact with the

superior shaft of the sledge, then, with the rotation of the exo-arm

following the elbow’s direction of extension, it tends to lift the sledge

vertically.

- Phase 2. The sledge reaches an altitude that allows it to rise autonomously,

it rises until the bar with the circular ramp comes into contact with the

lower ramp of the exo-arm. This way, the spring-arm is hooked to the exo-

arm and begins to pull it helping the patient in the elbow’s extension

Chapter 2

22

Figure 2.7 Schematic representation of the beginning of the hooking phase 1:

the ramp of the exo-arm (orange) enters in contact with the superior shaft of

the sledge (yellow)

Figure 2.8 Schematic representation of the beginning of the hooking phase 2:

the inferior shaft (yellow) starts to climb the step of the support disc (red) by

itself

Device description

23

Figure 2.9 Schematic representation of the end of the hooking phase 2: the

ramp of the sledge (yellow) enters in contact with the inferior ramp of the exo-

arm (orange)

The release procedure is much simpler than the previous one and is substantially

entrusted to the support disk. As said the support disc has at the point of release a

circular ramp. So, when the sledge will reach it, it would tend to decline in altitude

disengaging the exo-arm, now free to go back. The support disc then has a second

vertical wall to prevent the sledge to go beyond the release point.

Figure 2.10 Schematic representation of the start of the releasing phase: the

inferior shaft of the sledge (yellow) comes to the ramp of the support disc (red)

Chapter 2

24

Figure 2.11 Schematic representation of the releasing phase: The sledge

(yellow) starts to go down following the ramp of the support disc (red)

Figure 2.12 Schematic representation of the releasing phase: The sledge

(yellow) completed the descendent and the exo-arm (orange) is free to come

back

Device description

25

We complete the paragraph explaining the last part of the charge process for

completeness. As mentioned this stage presents many less complexity compared

to the discharging phase. It starts when the part of exo-arm opposite to the ramps

comes in contact with the contact plate of the charging block (blue in the figure

(2.13)).

Figure 2.13 View of the recharging-block with highlighted in blue the contact

plate

We see on the figures (2.14), (2.15), (2.16), (2.17), (2.18) the phases of the

charging process:

1. Once ended the releasing phase, the exo-arm is free to move and begin the

returning phase.

2. At the established point the exo-arm will come into contact with the plate,

we have already said that the plate is rigidly secured to the spring-arm with

screws.

3. Continuing its run, the exo-arm will push the plate back recharging the

spring.

4. When the patient's arm reaches full flexion the device will be in the

situation illustrated in the figure (2.18).

5. A small spring placed between the support of the spring-arm and the

sledge press this constantly downwards, which means that it will drop to

the lower level once left the step of the support disk.

6. With the sledge locked by the step of the support disk, the device is at the

starting point.

Chapter 2

26

Figure 2.14 Schematic representation of the charging phase: Finished the phase

of discharge the exo-arm (orange) is free to move and comes back during the

flexion movement

Figure 2.15 Schematic representation of the charging phase: The exo-arm

(orange) enters in contact with contact plate (blue)

Device description

27

Figure 2.16 Schematic representation of the charging phase: The exo-arm

(orange) pushes the contact plate (blue) so the sledge (yellow) goes up the

ramp of the support disc (red) and goes forward the hooking point

Figure 2.17 Schematic representation of the charging phase: The sledge (yellow)

comes in proximity of the step of the support disc (red)

Figure 2.18 Schematic representation of the charging phase: The sledge falls

down in the hooking point of the support disc (red) pushed by the contrast

spring

Chapter 2

28

Mechanism regulation

So far we have considered all the ranges of work, charge and discharge constants

for the sake of simplicity, of course, if this were true, it would violate one of the

required technical specifications, which provides for the possibility to adjust the

device in order to personalize the therapy. So, before continuing, let's make a brief

digression over the settings that can be performed on the device.

First, it should be pointed out that the angular distance to be traveled in the

recharging phase is slightly greater than the distance traveled in the discharging

phase; in fact, in order to recharge, the spring must travel the same stretch and in

addition there will be the part concerning the releasing mechanism.

Stated this, we get a first constraint on the range of adjustment, in fact, once

decided the range of discharge, the recharging one is directly derived.

Now let's see the maximum and minimum values for each range and where they

come from:

- The maximum value of the working range is 120 ° and is directly derived

from the maximum excursion that the exoskeleton arm can made together

with the patient.

- The sum of the maximum values of charge and discharge mustn’t be

higher than 120°, so, assuming for simplicity that the two ranges have the

same values, they will both have a maximum value of 60°.

- The minimum values are given substantially by the impediment caused by

the adjustment mechanism itself. Since a minimum of 20° is the value that

was established for the range (refer to section 3.2 for sizing details), we

obtain a minimum working range of 40° (20° + 20°).

- For the points of start and end of the charging and discharging range, the

mandatory constraints are the end of the working range towards the

extension for the release point and the point of maximum deflection

reached by the patient for the charging point.

We enter at this point into the merits of the design choices. So far we have treated

the settings that the device allows referring to the patient's workspace (0° to 120°).

Actually the device has a gear transmission that allows to take advantage of a

broader working space. Thanks to this, the working range is almost doubled

during the setting process, allowing a better accuracy.

From a functional point of view, we can distinguish three compartments used for

setting:

Device description

29

Releasing compartment – Used to adjust the maximum extension. It consists of

two coaxial discs arranged one above the other. Referring to the figures (2.19) and

(2.20), the first (dark blue) is bound to the device and is therefore fixed. The

second (blue light) mounts above it the releasing block (red) allowing to decide

the position of the releasing point and consequently the maximum extension.

Once set, they are locked by means of a screw on the outer ring.

Figure 2.19 View of the releasing compartment: Extreme position in extension

Figure 2.20 View of the releasing compartment: Extreme position in flexion

Chapter 2

30

Hooking compartment – Used to adjust the discharge range. It consists of two

coaxial components as before to which were added two arms connected as shown

in the figures (2.21) and (2.22); the two discs and the arms make up an articulated

parallelogram. The lower disc is the one that bears the release block while the

upper one host the hooking one. The function of the arms is to provide support to

the sledge of the arm spring to prevent it from falling in altitude and being released

from the exo-arm. Again, once chosen the hooking point and consequently the

range of charging, the discs are tightened together by a screw.

Figure 2.21 View of the hooking compartment: Position of minimum extension

Figure 2.22 View of the hooking sector: Position of maximum extension

Device description

31

Charging compartment – Used to adjust the working range. Once defined the

maximum extension point and the range of discharge, it only remains to set the

maximum flexion point. In order to do so, we shaped a coaxial disk to fit in the

block of charging and then fixed it with a screw on the spring-arm. The setting of

this component needs to be done with the spring loaded, or at least with the sledge

of the spring-arm blocked on the hooking block; this way it will be possible to

choose the point of maximum flexion by adjusting the diskette.

Figure 2.23 View of the charging compartment: In blue the charging-block

Chapter 2

32

Transmission and regulation of the torsional spring

In the previous section we focused more on the geometrical adjustments of the

device, we now turn to the dynamic adjustments. As already said several times,

the device uses a torsional spring for storing the energy; this spring is not directly

mounted on the device, but uses of a wire transmission. The main reason for this,

is the intrinsic behavior of the springs since, as we know, they have a linear trend

for the force or torque exerted as a function of elongation [16]:

𝐹 = 𝑘 ∙ 𝛥𝑙 (2.1)

This behavior is bad for the function that the spring has in the device, since torque

should be as uniform as possible. We analyzed the case in which the spring was

mounted without transmission taking into account that generally the torsional

springs allow a maximum deflection of 270°; What we have seen is that, if we

think that in order for the patient to make a 30° extension with the aid of the spring

our device accomplishes about 60° (assuming the use of spring loaded to the

maximum), the patient will get the maximum torque at the beginning of the

process (where he has less difficulty) and only 77% at the end. Moreover, the

possibility of torque adjustment in this case would be very limited.

Considered this issues it was chosen to introduce a transmission for the spring, in

order to maintain the drop of the torque to less than 10% when used in the worst

case (60° of excursion of the patient's arm). To save space and simplify the device,

it was chosen to introduce an unconventional transmission; taking advantage of

the spring geometry and considering the fact that it has always an excursion

inferior to 40° (for the actual sizing, see the paragraph 3.3), it was decided to

connect the upper arm of the spring to the shaft of the spring-arm by a cable as

shown below.

Speaking about the regulation of the torque exerted by the spring, it will be

regulated through another coaxial disk connected to the spring and place under it,

to which the lower arm of the spring will be bound once decided the setting (by

means of a screw).

Device components list

In this section we present the list of the device components. The following table

shows all the elements present in the device, or to ensure its functionality, both

those designed on purpose and the ones chosen from the catalog, such as bearings,

snap rings, screws and gears. The list is structured by dividing the components

into macro-groups that bear the names used during the discussion. The members

chosen from the catalog does not have the brand names but a summary of the

Device description

33

characteristics necessary for the installation and operation. Particular mention

goes to ball bearings, they have been chosen from the catalog just for their size,

since no wear test was needed considering neither static nor dynamic resistance,

because the loads involved are extremely low and the speed of rotation is not even

comparable to those that may undermine the component.

Device elements list divided in functional groups

Macro group Under category Component

Exo-arm Exo-arm Exo-arm

Spring-arm

Support

Shaft

Key, L 3 mm H 5 mm

Seeger, 3 mm x2

Washer, Dint 4mm Dext 12 mm

Screw, M4x10 mm

Seeger 8 mm

Contrast spring

Sledge

Internal horizontal arm

External horizontal arm

Internal sledge support

External sledge support

Inferior shaft

Superior shaft

Ramp-bar

Seeger, Dint 3 mm x3

Charging-block

Setting disc

Contact plate

Screw, M3x8 mm x2

Screw M5x8 mm

Support disc

Base Disco base

Screw, M5x8 mm x2

Releasing

compartment

Releasing disc

Releasing block

Quadrilateral arm releasing side

Screw, M2x5 mm countersunk head x3

Screw, M5x8 mm

Chapter 2

34

Hooking

compartment

Hooking disc

Hooking block

Quadrilateral arm hooking side

Screw, M2x5 mm countersunk head x3

Screw, M5x8 mm

Contour elements

Rotation supports

Ball bearing, Dint 8 mm Dext 12 mm H

3.5mm x2

Bushing, Dint 8 mm Dext 11 mm H 6mm

Gear transmission

Pinion, Dp 18 mm H 10 mm

Bull gear, Dp 36 mm H 10 mm

Transmission shaft exo side

Spring

transmission

Torque spring, Def max 270° Torque max

5000 Nmm

Wire transmission, Lmin 26 mm

Torque setting disc

Screw, M5x8 mm

Chapter 3

Device sizing

Genera sizing

After having analyzed the operation of the various parts of the device, in this

chapter we focus attention on the sizing of the various components. In particular,

in this paragraph we focus on the dimensions of the support disc and the size of

the circular ramps of the Exo-arm and the sledge. The device is largely

parameterized and the current size is due to the maximum forces that the device

must be able to support. A key note before we begin this journey concern the

technical specifications on the basis of which we went to size the components.

The maximum applicable torque which has made the sizing, 𝐶𝑚𝑎𝑥 = 2000 𝑁 ∙𝑚𝑚, is a very conservative value since this is the torque necessary for a healthy

person to move the arm horizontally [17], [18], [19], [20]. Once realized the

device will run tests to verify its performance, it is expected these will lead to a

reduction of this value. In fact, the purpose of the device is to provide an aid to

the patient not to move the limb in his place; limb that will, however, already

relieved of a part of its weight, balanced by the exoskeleton.

Sizing of the circular ramps

The geometry of these ramps is quite complex and deserves a certain deepening.

The first thing to note is that the angle of inclination of the ramp is not constant,

in fact, maintaining constant the height difference between the start and end of the

ramp and the angle of the circular sector in which the ramp develops, the angle of

inclination increases approaching the center, as seen in figure (3.1).

Chapter 3

36

Figure 3.1 Example of circular ramp, prospected view on left and lateral view on

right

Drawbacks due to this variation of the angle of inclination have been taken into

account. The superior shaft of the sledge has a convexity in the middle, in order

to come into contact with the ramp at its midpoint, and not on the inner rim where

it would touch if the shaft was simply cylindrical. We wanted to prevent this from

happening in first place for a more homogeneous distribution of the stresses on

the surface and then because a smaller angle inclination allows the ramp to raise

the sledge with less effort. In fact, greater the inclination greater will be the effort

made by the shaft to slide on the ramp.

The first step for the sizing of the ramp is the choice of the diameter of the sledge

inferior shaft, it determines the vertical translation which the sledge must fulfill.

The shaft diameter d and, consequently the height of the step h, was chosen on

the basis of the FEM analysis (for FEM analysis please refer to the section 3.4)

and the following value was chosen:

𝑑 = ℎ = 3 𝑚𝑚

This dimension is one of the parameters on which we will sizing the circular

ramps of Exo-arm. Choosing the distance ℎ given by the shaft we are going to

size the ramp imposing other two dimensions, the slope of the ramp in the medium

radius α and the angle of the circular sector at the base of the ramp 𝛽.

We suppose you draw on a plane the surface of the ramp taken in its middle range,

it will be a right triangle whose base 𝑏 is function of 𝛽 and the medium radius 𝑅𝑚

according to the following equation

𝑏 =2 ∙ 𝜋 ∙ 𝑅𝑚 ∙ 𝛽

360° (3.1)

Known 𝑏 and ℎ, the inclination angle 𝛼 is given by

Device sizing

37

𝛼 = tan−1 (ℎ

𝑏) (3.2)

We chose to use the following values for 𝛼 and 𝛽:

𝛼 = 30° 𝛽 = 10°

At this point it is possible to find the medium radius through the following relation

𝑅𝑚 =ℎ ∙ 360°

tan(𝛼) ∙ 2 ∙ 𝜋 ∙ 𝛽 (3.3)

We obtain 𝑅𝑚 = 30 𝑚𝑚

This value is very important, in fact we will use it not only to size the circular

ramps but will also serve for the setting mechanism and more generally imposes

the size that will have the entire device. The ramps width will be dimensioned

later on the basis of a stress analysis. In fact, although this dimension does not

appear in the geometrical design of the device, it is fundamental for the

functioning because both the superior and the inferior ramp must be able to

support the entire load of the spring, as we will see in section 3.4. In view of the

technical difficulties for the realization of a component with a similar geometry

we will try to maintain this dimension as small as possible.

Sizing of the sledge kinematism

The sledge that deals of the hooking and releasing of the torsional spring is

actually an articulated parallelogram. For this reason, it presents some more

project problems respect to a sledge with a simple vertical translation. Referring

to the figure (3.2), the side of the parallelogram called for simplicity sled is the

side 𝑐, it is always maintained vertical, but its mean point rotates around the mean

point of the side 𝑎 that connects the two support joints.

Chapter 3

38

Figure 3.2 View of spring-arm with highlighted in red the sides of the articulated

parallelogram

Always referring to the figure (3.2), we chose to keep the lock position of the

sledge, then at its lowest height, 𝛼 = 0 because, being the Spring-arm always

under load with a torque which pulls it in a clockwise direction (to the left in the

figure), it will tend spontaneously to go towards 𝛼 = 0 being this the point where

𝑐 is more distant from 𝑎 and the equilibrium position. So if we had chosen a

different 𝛼 value the sled was not be stable in the blocking position but it would

tend to get up by itself. The size of 𝑏 and 𝑑 (𝑏 and 𝑑 must be equal) has been

chosen in order to use all the allowed space in the device to minimize the distance

of 𝑐 from the vertical axis. In this way the approximation with a purely vertical

motion will be the best possible.

Referring now to the figure (3.3) we derive the relationship between the length 𝑏

and the distance between ℎ and the vertical axis called 𝑑, with ℎ the height of the

hooking-block step.

Device sizing

39

Figure 3.3 Scheme for the calculation of the horizontal movement of the sledge

𝑑 = 𝑏 ∙ (1 − cos(𝛼)) (3.4)

ℎ = 𝑏 ∙ 𝑠𝑖𝑛(𝛼) (3.5)

Actually, after a first sizing, b is resulted bounded for reasons due to the overall

dimensions of the device for which it was obtained 𝑏 = 12 𝑚𝑚 and then 𝑑 =0,38 𝑚𝑚 little more than 10% of ℎ then an acceptable value.

Sizing of the setting mechanism

As mentioned in section 2.4, the setting mechanism of the discharge range is an

articulated quadrilateral. For his sizing we refer to the figure which highlights in

red the four sides of the parallelogram and in blue and the circumferences of the

mean radius 𝑅𝑚 , that we calculated in the previous paragraph, and those of

maximum and minimum radius 𝑅𝑚𝑖𝑛 and 𝑅𝑚𝑎𝑥, respectively. These last two radii

are those that will determine the final length of the sledge shafts and consequently

will affect the sizing of the spring-arm and the final size of the device.

Chapter 3

40

Figure 3.4 View of the setting mechanism for the range of discharge with

highlighted in red the articulated quadrilateral

The goal that has been pursued during the dimensioning of this mechanism is to

try to reduce to the minimum the size, looking for the dimensions of the arms such

that 𝑅𝑚𝑎𝑥 is minimized.

According to the project specifications, the angular range in which it must be

possible to adjust the device about the discharging phase is [20°÷60°]. After a first

sizing of it we obtained that, for lack of space we will have a minimum angle

𝛼𝑚𝑖𝑛 = 39°. We have therefore chosen to have a maximum angle 𝛼𝑚𝑎𝑥 = 117° in order to subsequently insert a gear transmission between the device and the

exoskeleton which allows to obtain the desired range.

Actually 24° of the 39° are not due to the size of the mechanism arms but to the

hooking and releasing blocks, then the mechanism has been sized in the range

𝛼 = [15° ÷ 93°].

Known the angles 𝛼𝑚𝑖𝑛, 𝛼𝑚𝑎𝑥 and the mean radius 𝑅𝑚, we derive a system of

equations to calculate the lengths of the sides 𝑎, 𝑏, 𝑐, 𝑑 and the 𝑅𝑚𝑎𝑥 and

𝑅𝑚𝑖𝑛 radii. We know also that

Device sizing

41

𝑎 = 𝑑

𝑏 = 𝑐

𝑅𝑚 =𝑅𝑚𝑎𝑥 + 𝑅𝑚𝑖𝑛

2

(3.6)

Geometrically it is obtained that for the same length of 𝑎 is minimized 𝑏 and

consequently 𝑅𝑚𝑎𝑥 imposing that, when 𝛼 is maximum, the midpoint of side 𝑏

lies on the circumference of radius 𝑅𝑚𝑖𝑛and that 𝑏 is tangent to this as shown in

figure (3.5).

Figure 3.5 Scheme 1 for the design of the setting mechanism for the discharging

range

Note that the segment that connects the midpoint of the side 𝑏 and 𝐴 is equal to

𝑅𝑚𝑖𝑛 for construction. Moreover, always for construction this segment is

perpendicular to b.

We obtain that:

𝑅𝑚𝑖𝑛 = 𝑎 ∙ cos (𝛼𝑚𝑎𝑥4

) (3.7)

𝑏 = 2 ∙ 𝑎 ∙ sin (𝛼𝑚𝑎𝑥4

) (3.8)

Considering instead the situation in which 𝛼 is equal to 𝛼𝑚𝑖𝑛 , we have the

Chapter 3

42

situation in figure (). We can see how in this case 𝑅𝑚𝑎𝑥 is equal to the distance

between 𝐴 and 𝐶.

Figure 3.6 Scheme 2 for the design of the setting mechanism for the discharging

range

We obtain:

𝑅𝑚𝑎𝑥 = 𝑎 ∙ cos (𝛼𝑚𝑖𝑛2) + √𝑎2 ∙ (sin (

𝛼𝑚𝑖𝑛2))

2

+ 𝑏2 (3.9)

At this point we have found the following system of equations:

{

𝑅𝑚 =

𝑅𝑚𝑎𝑥 + 𝑅𝑚𝑖𝑛2

𝑅𝑚𝑖𝑛 = 𝑎 ∙ cos (𝛼𝑚𝑎𝑥4

)

𝑏 = 2 ∙ 𝑎 ∙ sin (𝛼𝑚𝑎𝑥4

)

𝑅𝑚𝑎𝑥 = 𝑎 ∙ cos (𝛼𝑚𝑖𝑛2) + √𝑎2 ∙ (sin (

𝛼𝑚𝑖𝑛2))

2

+ 𝑏2

(3.10)

Solving we find the following relations

Device sizing

43

{

𝑎 = 𝑑 =

2 ∙ 𝑅𝑚

cos (𝛼𝑚𝑎𝑥4 ) + cos (

𝛼𝑚𝑖𝑛2 ) + √(sin (

𝛼𝑚𝑖𝑛2 ))

2

+4 ∙ (sin (𝛼𝑚𝑎𝑥4 ))

2

𝑏 = 𝑐 = 2 ∙ 𝑎 ∙ sin (𝛼𝑚𝑎𝑥4

)

𝑅𝑚𝑖𝑛 = 𝑎 ∙ cos (𝛼𝑚𝑎𝑥4

)

𝑅𝑚𝑎𝑥 = 2 ∙ 𝑅𝑚 − 𝑅𝑚𝑖𝑛

(3.11)

We found the following values

𝑎 = 𝑑 = 21,1 𝑚𝑚 𝑏 = 𝑐 = 20,6 𝑚𝑚 𝑅𝑚𝑖𝑛 = 18,4 𝑚𝑚 𝑅𝑚𝑎𝑥 = 41,6 𝑚𝑚

Transmissions design

As mentioned in chapter 2 the device includes two transmissions that connect this

to the exoskeleton and to the torsional spring. A good gain in terms of space was

achieved by placing coaxially the two transmissions. Furthermore, if for the

connection between the exoskeleton and the device Exo-arm we propose a gears

transmission with straight teeth, to the side of the torsional spring we have chosen

to connect the rod of the spring to the device Spring-arm with a wire. The sizing

of this second transmission is far less immediate than the first and deserves a

detailed discussion.

Sizing of the gear transmission

Let's start with the sizing of the gear transmission. As already mentioned, we have

not been able to maintain a direct transmission due to the encumbrance of the

components.

Required range: 20° ÷ 60° Minimum value due to encumbrances in the device: 39° Maximum angle necessary for the device:

𝑎𝑛𝑔𝑑𝑒𝑣,𝑚𝑎𝑥 =60° ∙ 39°

20°= 117° (3.12)

We also get a gear ratio

Chapter 3

44

𝑟 =117°

60°= 1,95 (3.13)

For simplicity we take 𝑟 = 2

We get the following ranges

𝑎𝑛𝑔𝑒𝑥𝑜 = 19,5° − 58,5° 𝑎𝑛𝑔𝑑𝑒𝑣 = 39° − 117°

The toothed wheel with the smaller diameter in the catalog, without going to

search for particular pieces, has a pitch diameter equal to 𝐷𝑝,𝑝𝑖𝑛𝑖𝑜𝑛 = 18 𝑚𝑚.

This is the pinion and must be shrunk on the Exo-arm. Since the diameter of the

pinion is less than the minimum one of the sledge, it was possible to save space

by mounting the gear just below the height in which the Ramp-arm works (see

figure (3.7)).

Therefore, having to maintain a ratio of the gear 𝑟 = 2 the pitch diameter of the

bull gear will be 𝐷𝑝,𝑏𝑢𝑙𝑙 𝑔𝑒𝑎𝑟 = 36 𝑚𝑚 [22].

Figure 3.7 View of the gear transmission of the device, in grey the bull gear and

in orange the pinion

Device sizing

45

Design of the spring transmission

Now let’s move to the sizing of the torsional spring transmission.

Having decided that the torsional spring is coaxial to the axis of the bull gear, we

know that the distance between the spring axis of rotation and that of the Spring-

arm is imposed by the gear transmission and equal to

𝑑 =18 + 36

2= 36 𝑚𝑚 (3.14)

To maintain the torque transmitted as linear as possible during the operation of

the device, we imposed that, with the maximum discharging range of the device

had a reduction of the transmitted torque lower than the 10%. Since this is the

worst case, in case of the lower range will result a less reduction. Assuming to

choose a spring with a maximum deflection of 270 ° we obtain the following

parameters:

Maximum deflection: 𝐷𝑒𝑓𝑚𝑎𝑥 = 270° Maximum deflection admitted: 𝐷𝑒𝑓𝑚𝑎𝑥,𝑎𝑑𝑚𝑖𝑡 = 270° ∙ 10% = 27° Maximum angular range of the spring-arm: 𝛼𝑑𝑒𝑣,𝑚𝑎𝑥 = 117°

Transmission ratio: 𝑟 =117°

27°= 4.33

The diameter of the spring-arm shaft is 𝐷𝑠ℎ𝑎𝑓𝑡 = 8 𝑚𝑚, so the diameter at which

we will have to connect the wire to the spring rod will be

𝐷𝑠𝑝𝑟𝑖𝑛𝑔 = 4,33 ∙ 8 = 34,64 𝑚𝑚

Having available more space, we decided to bring the diameter 𝐷𝑠𝑝𝑟𝑖𝑛𝑔 =

40 𝑚𝑚, obtaining a transmission ratio 𝑟 = 5.

So we obtain 𝐷𝑒𝑓𝑚𝑎𝑥,𝑎𝑑𝑚𝑖𝑡 = 23.4° We dimensioned the spring and the transmission ratio as if it is constant, this is

true for normal transmissions such as the gears one sized above, it is not

absolutely true for the transmission of the spring which has the appearance shown

schematically in figure (3.8).

Chapter 3

46

Figure 3.8 Schematic representation of the torque spring transmission, in grey

the torque spring, in yellow the Spring-arm shaft and in red the wire who

connects the previous elements

The first thing that we have verified in phase of the project is that there was a

fairly wide range in which the transmission ratio was constant. First we search the

mathematical relationship that connects the rotations of shaft and spring. We refer

to the figure (3.8) calling the radius of the torsion spring at the point where the

wire is connected, 𝑅1, and the radius of the spring-arm shaft, 𝑅2. We derive the

mathematical relationship between the length 𝑠 to the rotation 𝛼, this greatly

simplifies the geometry of the problem. It is also easy to show that

𝑙 = √𝑠2 − 𝑅22 (3.15)

This is because the wire will always be tangent to the shaft and thus will be

perpendicular to the radius 𝑅2 at the contact point 𝐵. We project the segment 𝑂1𝐵

on the segment 𝑂1𝑂2 and on its traverse passing for 𝑂1. We call the two

projections 𝑠𝑦 and 𝑠𝑥 respectively. These projections are function of 𝛼 as follows:

Device sizing

47

{𝑠𝑥 = 𝑅1 ∙ sin(𝛼)

𝑠𝑦 = 𝑅1 ∙ cos(𝛼) + 𝑑 (3.16)

Where 𝑑 is the length of the segment 𝑂1𝑂2.

We obtain

𝑠 = √𝑠𝑥2 ∙ 𝑠𝑦2 = √𝑅12 ∙ (sin(𝛼))2 + (𝑅1 ∙ cos(𝛼) + 𝑑)2 (3.17)

By combining the formulas (3.15) and (3.17) we get the graph of 𝑙 in function of

𝛼 (figure (3.9)).

Figure 3.9 Graphic of the length l in function of the angle α

We call 𝛽 the rotation of the shaft and 𝑑𝑙 the difference between 𝑙 and 𝑙𝑚𝑖𝑛 where

𝑙𝑚𝑖𝑛 = 𝑙(𝛼 = 180) = 12 𝑚𝑚. We have that

𝛽 =𝑑𝑙 ∙ 360°

2 ∙ 𝜋 ∙ 𝑅2 (3.18)

Chapter 3

48

The reason why we use 𝑑𝑙 instead of 𝑙 is due to the fact that 𝑙𝑚𝑖𝑛 does not

intervene in the rotation 𝛽 because it never arrives to wind on the shaft.

Figure 3.10 Graphic of the angle β in function of the angle α

We calculate at this point as change the transmission ratio 𝑟 in function of 𝛼

𝑟 =𝛽(𝛼 + 𝑑𝛼) − 𝛽(𝛼)

𝑑𝛼 (3.19)

Device sizing

49

Figure 3.11 Graphic of the ratio r in function of the angle α

The analysis clearly shows a maximum in the transmission ratio for 𝛼 = 141,3° with 𝑟 = 5,14 (see figure (3.11)). In this area, how we can also see in the

previously graphs (figure (), figure ()), is present a range where the dependence

of 𝛽 from 𝛼 tends to be linear.

At this point it remains to calculate the effective range in which the spring-arm

moves. In fact, we will have to take into account the maximum extremes that the

spring-arm sledge can reach in all configurations. We place equal to 120° ∙ 2 =240 ° the maximum extension point, it is definitely one extreme of the range we're

looking for. We can find the other extreme setting the device with the minimum

discharge range and the minimum working range, which means in the user's

coordinates, where 0° is the maximum deflection, a discharging range of 20° and

a working range of 40° (the double the discharging range). We will have that the

second extreme will be 20° which multiplied by the reduction ratio becomes 40° then the actually range where the spring-arm operate will be

𝑑𝛽 = 240° − 40° = 200°

Dividing this value by the reduction ratio that we have seen to be around 5 in the

Chapter 3

50

peak, we get the width of the range in which the spring-arm will operate

𝑑𝛼 =200°

5= 40°

Then we are looking for a range for 𝛼 of 40° in which the transmission ratio is as

high as possible. We have done an optimization researching the maximum

average value of 𝑟 on 40° in the range of [0° ÷ 180°]. We found the following

range

𝛼 = [117,2 ÷ 157,2]

We will need to forecast two limits positioned in the locations found. The average

final ratio is

𝑟𝑚 = 5,031

As concern the maximum torque transmitted by the spring, it will have to take

account of transmission ratios. Having to obtain a maximum torque at patient's

arm of 2000 𝑁 ∙ 𝑚𝑚, this will be 1000 𝑁 ∙ 𝑚𝑚 at the device level and will rise

to 5000 𝑁 ∙ 𝑚𝑚 at the level of the torsional spring. Therefore, the researched

torsional spring will have the following characteristics:

Maximum deflection: 270° Torque at the maximum deflection: 5000 𝑁 ∙ 𝑚𝑚

Torsional stiffness: 18,52 𝑁 ∙ 𝑚𝑚/𝑑𝑒𝑔

FEM analysis of the most stressed components

We speak in this section of the FEM analysis that were conducted to size or test

the components in which the concentration of stress is greater. These components

are essentially all the elements that make up the sledge, which is undoubtedly the

critical component of the entire device since it is constantly subjected to the forces

generated by the spring. Furthermore, its components have the resistant sections

that are inferior. Other components that need to be checked are the ramps of the

exo-arm since they present the same characteristics of the sledge as state above.

Sizing of the inferior shaft of the sledge

We introduced at the beginning of the second chapter that at the core of all the

sizing procedure of the device there is the diameter of the inferior shaft of the

Device sizing

51

sledge. This has been sized by simply analyzing the finite elements in order to

seek the minimum diameter to withstand the maximum load provided by the

spring. For simplicity the shaft was assumed to be bound completely

(interlocking) to both ends and subject to load in its central part.

The finite element analysis was conducted with the Autodesk Inventor

Professional 2015 software, and the results are the following:

A first analysis was made assuming a shaft diameter of 2 mm.

Stated this value all the sizing step previously presented were followed in order

to find the length that it should have and its part subjected to the load (useful

length). The dimensions used are:

Diameter: 𝐷 = 2 𝑚𝑚

Total length: 𝐿𝑡 = 19,5 𝑚𝑚

Useful length: 𝐿𝑢 = 15,5 𝑚𝑚

2 mm are left outside to each end where the lateral supports come into contact.

The maximum stress situation is the one in which the spring is charged with the

total torque required, equal to 𝐶 = 1000 𝑁 ∙ 𝑚𝑚. Furthermore, by the sizing, it

resulted a medium radius of 𝑅𝑚 = 20 𝑚𝑚; Therefore, the medium strength

applied is equal to

𝐹 = 𝐶/𝑅𝑚 = 50 𝑁.

In figures (3.12), (3.13), (3.14) are reported the images with the results obtained

in terms of Von Mises stress, displacement and Safety Factor, respectively (the

component was assumed to be made of steel) [23].

Chapter 3

52

Figure 3.12 FEM analysis of the inferior shaft first design, Von Mises Stress

arrangement

Figure 3.13 FEM analysis of the inferior shaft first design, Displacement

arrangement

Device sizing

53

Figure 3.14 FEM analysis of the inferior shaft first design, Safety Factor

arrangement

As easily predictable the greater part of the stress is at the interlocking point, and

it has a maximum value of Von Mises of 302,5 𝑀𝑝𝑎. This generates a minimum

Security Factor of 0,68. Even if this model is very conservative a value of 0,68 is

not acceptable and, in general, any value inferior to 1 would be not acceptable. So

it was decided to use a security value for the shaft of 1,5.

The test was then repeated with a diameter value of 3mm.

Recapping:

Diameter: 𝐷 = 3 𝑚𝑚

Total length: 𝐿𝑡 = 27,65 𝑚𝑚

Useful length: 𝐿𝑢 = 23,2 𝑚𝑚

Applied strength: 𝐹 = 1000/30 = 33,33 𝑚𝑚

The results with these values are shown in figures (3.15), (3.16), (3.17).

Chapter 3

54

Figure 3.15 FEM analysis of the inferior shaft final design, Von Mises Stress

arrangement

Figure 3.16 FEM analysis of the inferior shaft final design, displacement

arrangement

Device sizing

55

Figure 3.17 FEM analysis of the inferior shaft final design, Safety Factor

arrangement

We can see that at an increase of the diameter corresponds an increase in the arm

and a decrease in the strength if the torque is kept constant. For this reason, the

effort value grows significantly with the variation of the diameter and the security

values results in 2,39, clearly superior to the 1,5 required. It has to be taken into

consideration however that the device will be realized with the 2 mm diameter if

the torque actually used were to be inferior.

The superior shaft bears the same characteristics of the inferior one except for the

small convexity at the center, so we avoid to report its analysis because not

interesting. Moreover, the superior shaft is the pin for the parallelogram and needs

two Seeger to bound the axial translation. The commercial Seeger have a diameter

minimum of 3 mm and this represents a limitation to the willingness of look for

inferior diameter.

Sizing of the circular ramps of the exo-arm

When we described the geometrical sizing of the circular ramps in paragraph 3.1,

we didn’t stet any limitation for their width. In fact, as state above, the width is

limited only by the load that the component needs to withstand. Realistically any

value inferior to the distance between the two supports that prevents the ramp

from flexing would be good. It’s worth reminding that the distance mentioned

does not depends over the width of the ramps.

Starting with the superior ramp, the values used are:

Chapter 3

56

Width of the ramp: 𝑏 = 10 𝑚𝑚

Torque applied: 𝐶 = 1000 𝑁 ∙ 𝑚𝑚

Average arm: 𝐿 = 30 𝑚𝑚

Average strength: 𝐹 = 𝐶/𝐿 = 33,33 𝑁

If the sledge was to move only vertically, this analysis wouldn’t be necessary,

since the superior ramp would have to face only the rolling friction strength

created by the contact between the inferior shaft and the hooking block (plus a

little strength generated by the spring pushing the sledge against the support disc).

However, being the sledge part of an articulated parallelogram, the superior ramp

to raise needs to face the strength generated by the torsional spring. So, we will

use the maximum torque in this analysis.

The results:

Figure 3.18 FEM analysis of the exo-arm superior ramp, Von Mises Stress

arrangement

Device sizing

57

Figure 3.19 FEM analysis of the Exo-arm superior ramp, displacement

arrangement

Figure 3.20 FEM analysis of the Exo-arm superior ramp, Safety Factor

arrangement

We see that, in contrast with the case of the inferior shaft of the sledge in which

we were interested in the safety factor to avoid the failure of the component, in

this case we are interested in the downward displacement of the ramp. In fact, an

excessive displacement would prevent the sledge to raise enough to overcome the

step of the hooking block before the ramp ends. In any case we see that, already

Chapter 3

58

in the first attempt, with a 10 mm width, the displacement is less than one tenth

of a millimeter.

With a similar situation, the inferior sledge width is enough to allow a good

operation even with larger displacement.

We report the results obtained by the FEM analysis for completeness:

Figure 3.21 FEM analysis of the Exo-arm inferior ramp, Von Mises Stress

arrangement

Device sizing

59

Figure 3.22 FEM analysis of the Exo-arm inferior ramp, displacement

arrangement

Figure 3.23 FEM analysis of the Exo-arm inferior ramp, Safety Factor

arrangement

Chapter 3

60

Check of the sledge ramp

We conclude with the verification of the third component that is the sledge ramp

that coupling with the exo-arm allows to this to be lulled by the spring-arm. Also

in this case we use the maximum spring torque. The width of this ramp is

irrelevant for the load to failure and displacement analysis, for this reason, the

width of this ramp is kept equal to those of the exo-arm ramps. The static strength

verification relates in this case the bar on which the ramp has been obtained. The

bar has the following dimensions:

Length: 𝐿 = 27,65 𝑚𝑚

Width: 𝐵 = 4,4 𝑚𝑚

Height: 𝐻 = 4 𝑚𝑚

We check then if with these values of first attempt the component presents

acceptable values of stress and displacement.

Figure 3.24 FEM analysis of the sledge ramp, Von Mises Stress arrangement

Device sizing

61

Figure 3.25 FEM analysis of the sledge ramp, displacement arrangement

Figure 3.26 FEM analysis of the sledge ramp, Safety Factor arrangement

Chapter 3

62

We get a maximum Von Mises stress value equal to 46,9 MPa, which corresponds

to a Safety Factor of 4,41 well beyond the minimum value sought and finally a

maximum displacement of 0.002 mm. The component is so well designed and do

not presents risks of failure.

Dynamic simulation with rigid bodies model

In this section we analyze the dynamic behavior of the system. It has been created

implementing a multi-body model of rigid body of the device using a software for

simulation: Autodesk Inventor Professional 2015.

Let's start with the description of model, since, to reduce the computational burden

of the simulations, it was generated a simplified version of the device. It provides:

- The set of components called in general the support disc was bound to a

range of discharging of 60°.

- A simplified version of the spring-arm, where all the rigidly connected

parts have been modeled as a single component.

- The exo-arm that results unchanged except for the lack of the gear

transmission that is not comprehended in the simulation.

Figure 3.27 View of the simplified model of the device used for the dynamic

simulation

Device sizing

63

Figure 3.28 View of the simplified model in order to see the contact between the

sledge inferior shaft and the Hooking-block in the simulation start point

In the figure it has been removed the upper arm of the parallelogram and the outer

side one of the sledge in order to allow a better view of the lock of the lower shaft

by the component called hooking-block.

What we see in the two figures is the starting point of the dynamic simulation. In

this simulation we verify the correct developing of the discharging phase, in

which the exo-arm is connected with the spring-arm until the releasing point at

the end of the phase.

In this simulation too, we have worked assuming the most critical situation that is

when the spring is at maximum charge. Furthermore, although the device

functions primarily with small inclinations with respect to the horizontal plane,

the gravitational strength has not been considered; in fact, in the real version, there

will be a small spring with the aim to always keep in contact the lower shaft of

the sledge with the support disc.

The purpose of the dynamic analysis was also to evaluate the force required by

the spring and, to do so, it was assumed that it should be sufficient to ensure

operation even in case of a 90° inclination over the horizontal plane. A higher

inclination is physically impossible and was not taken into account.

The analysis focused solely on the discharge phase, in fact, the other phases of

operation are extremely simple, and it was not considered necessary to invest

more time in their analysis.

On the contrary, the discharge phase is actually complex and deserves to be

investigated deeply to be sure of its correct operation.

We report the final set parameters, they originate from many tests that have

guaranteed the operation of the device and an improvement of its design even

before it was actual manufactured:

- Constant torque applied to the spring-arm: 𝐶 = 1000 𝑁 ∙ 𝑚𝑚.

- Force applied to the sledge: 𝐹 = 3 𝑁.

Chapter 3

64

It was also taken into account the dissipated forces due to the rubbing in the

parallelogram hinges; the value assumed is:

- Damping: 𝐷 = 5 𝑁 ∙ 𝑚𝑚 ∙ 𝑠/𝑑𝑒𝑔

In the simulation, in order to verify the forces acting on the exo-arm, this has a

rotation speed set to:

- Rotation speed: 𝜔 = 30 𝑑𝑒𝑔/𝑠

- Simulation time: 𝑡 = 2 𝑠

Our main interest in the multi body simulation is to seek torques developed during

the course of the simulation on the exo-arm. This, in fact, is mechanically

connected to the patient's arm through the exoskeleton and then the forces acting

on it will directly be transmitted to the user. Although ideally the trend of the

torque transmitted to the entire work cycle should resemble the one in the figure,

we know that even in the hooking phase the patient will have to exert a torque

enough to allow the sledge to rise. The evaluation of this torque at an analytical

level can be obtained by applying the principle of conservation of energy as

follows:

If the sledge was free to translate, we have calculated that the distance it would

travel would be: 𝑑 = 0.38 𝑚𝑚; however, since it is bound, this distance will be

traveled by the spring-arm and it will be equal to:

𝛼 =𝑑 ∙ 360°

2 ∙ 𝜋 ∙ 𝑅𝑚= 0,73° (3.20)

This formula has been used considering the torque of the torsion spring to be

constant. This hypothesis can be established since the transaction takes place in

few tenths of rotation degree.

Knowing the transmission ratio between the spring and the arm, 𝑟 = 5, the

rotation beta of the spring is equal to:

𝛽 =𝛼

5= 0,146° (3.21)

So the energy to be transmitted to the spring is:

𝐸𝑢 = 5000 ∙ 𝛽 = 730 𝐽 (3.22)

Device sizing

65

To this we need to add the dissipated energy due to the friction over the lower

shaft following the rolling friction model:

𝐹𝐻 = 𝑁 ∙ 𝑓𝑣 (3.23)

With N standing for the transversal load equal to 33.33N and 𝑓𝑣 standing for the

rolling friction coefficient (in the case of steel-steel friction) equal to 5 ∙ 10−3

𝐹𝐻 = 0,33 𝑁. To this we need to add the 3 N given by the contrast spring.

Assuming the movement of the sledge in the phase before it rises of 2 mm, the

energy dissipated by these two contributions are:

𝐸𝑑 = (3 + 0,33) ∙ 2 = 6,66 𝐽 (3.24)

On the other side, the patient employs the big part of the movement over the ramp

(width 10°) in order to lift the sledge; assuming that 7° are needed before the rise,

the actual ones for the patient are 3.5°. This means that the torque exert by the

patient should be:

𝐶𝑚 =𝐸𝑢 + 𝐸𝑑3,5°

= 210 𝑁 ∙ 𝑚𝑚 (3.25)

Figure 3.29 Graphic of the theoretical working cycle of the device in function of

the flexion angle

Chapter 3

66

We now report the results of the simulation in order to see if the calculations are

realistic.

Figure 3.30 Dynamic Simulation results: Torque transmitted to the user during

the discharging phase

The graph presents the trend of the torque exerted on the patient's arm as a

function of the independent coordinate alpha that is the advancement of the arm

from the starting point presented in the figure. In red is reported the average of

each value for each interval of 1°. You can see how, in the first phase, the

transmitted torque is negative since it is exercised by the patient. This phase lasts

approximately 4 °, then there is a zero torque space in which the sledge raises by

itself, but the ramp of the sledge is not yet come into contact with the ramp of the

lower exo-arm. After that the hooking occurs and the spring starts to drag the

patient's arm and the transmitted torque has a downward trend with the

advancement. Finally, after about 26° it is released and the torque falls to zero.

The peaks present in the graph during the discharging phase are probably due to

the interaction between the various rods of the adjusting quadrilateral, which have

created problems to the resolver during the computation.

Results:

Average value in the range [0° ÷ 4°]: −500 𝑁 ∙ 𝑚𝑚

Device sizing

67

Average value in 'interval [5° ÷ 25°]: 2000 𝑁 ∙ 𝑚𝑚

We report the performance of the elevation of the lower shaft of the sledge,

function of the independent coordinate 𝛼

Figure 3.31 Dynamic Simulation results: Sledge elevation during the discharging

phase

In the last graph that we present we can see how the transmitted torque to the exo-

arm changes in function of the elevation of the sledge. In particular, we see that

in the range between 2 and 3 mm no torque is applied to the arm. In fact, in this

zone, the sledge starts to autonomously rise and covers the little gap caused by

the movement of the superior ramp of the exo-arm and hooks to the lower one.

Chapter 3

68

Figure 3.32 Dynamic Simulation results: Torque transmitted in function of the

sledge elevation

Chapter 4

Prototype realization

Specification of the prototype

Once concluded the virtual prototyping phase, it was decided to design and realize

a prototype to effectively verify proper operation and feasibility. Being the

designed device very small, it has not been possible to reproduce it to its actual

size due to the lack in accuracy of the machines available at the institute; it was

therefore decided to develop a prototype with a larger size.

The prototype has followed the steps for dimensioning shown in the previous

chapter, however, the starting sizes were chosen arbitrarily in order to be easily

realized with the means available. Furthermore, the project was adapted in order

to use some mechanical parts, such as bush and bearings, which were already

present in the workshop.

Finally, since we wanted to verify only the good dynamics of the mechanism, it

was decided not to implement the adjustment mechanisms. In particular, it was

decided to create a support disc in a unique block with a fix and representative

settings of 30° for the charging and discharging range, and 120° for the working

range. Consequently, also the charging block of the spring-arm will have only one

mounting position instead of the entire expected range.

For the material, having available a 3D printer, it was decided to 3D print most of

the pieces and made with to machine tools (ones with numerical control) only

those that needed a more resistant material or with sizing tolerances more tight.

Assuming to use the same torsional spring, the loads present will be the same,

while the resistant surfaces will be higher; for this reason, it was decided to keep

valid the analysis of the efforts already made to the device without going in further

details.

We report now the list of the components used for the construction of the

prototype.

Chapter 4

70

Figure 4.1 Front view of the prototype

Figure 4.2 Rear view of the prototype

Parts produced with CNC

In this section we are going to preset the prototype parts that needs to be made of

metal by machine tools; these parts will be the ones more subject to efforts.

All the sledge components will be realized through chip removal as these are the

parts most stressed part of the entire structure.

The side supports of the sledge, and the two horizontal arms will be made of

aluminum since they do not require a particular resistance but a good dimensional

accuracy.

Instead, the two shafts will be made of brass to prevent the aluminum-aluminum

contact to seize up the mechanism. In fact, we remind that the aluminum-

aluminum contact is often cause of blocks due to the creation of micro-welds in

Prototype realization

71

response of the sliding of the two surfaces.

With regard to the ramp of the sledge, it will be hybrid; it will have a brass core

connected to the inner side arm, while the rest of the bar including the ramp will

be realized in 3D molded plastic.

The support shaft and the key will also be made of aluminum or steel.

Finally, the spring-arm is made of aluminum.

Parts produced with 3D printer

The parts made by 3D printing will instead be the support disc, in its version as a

single piece, charging support and block for the spring-arm is (also in one piece),

and finally the pedestal that will serve not only as support to the device but also

as installation set for the torsional spring.

We want to clarify that the parts produced as a single block will be created in the

geometry of the device in order to detect any issues that may be encountered

during operation due to them. Think, for example, to the arms of the adjustment

quadrilateral, which must support the slide during the discharge phase; if they are

not leveled, they could give tremors during the motion, especially in the joint

areas.

Prototype components list

Macro group Component Production Material

Exo-arm Exo-arm CNC Aluminum

Spring-arm

Main shaft CNC Aluminum

Key CNC Aluminum

Support 3D printing Plastic

Contrast spring Manual Steel

Horizontal arm x2 CNC Aluminum

Internal sledge support CNC Aluminum

External sledge support CNC Aluminum

Inferior shaft CNC Brass

Superior shaft CNC Brass

Ramp-bar core CNC Brass

Ramp-bar body 3D printing Plastic

Bushing Dint 3 mm Dext

5mm L 4 mm x2 CNC Aluminum

Chapter 4

72

Seeger 4 mm x3 Buying Steel

Screw, M3x6 mm x2 Buying Steel

Screw, M4x10 mm Buying Steel

Washer, Dint 4mm

Dext 12 mm Buying Steel

Support disc

Support disc 3D printing Plastic

Pedestal 3D printing Plastic

Screw, M5x8 mm x2 Buying Steel

Contour

elements

Bearing x2 Buying Steel

Bushing Buying Plastic

Torque spring Buying Steel

Chapter 5

Conclusion and future developments

Figure 5.1 View of the device mounted on the LIGHTarm exoskeleton

In conclusion, we can say that the presented device meets all the required

specifications satisfactorily, we have to make a few final comments on what has

been done and what will be the next phases of development.

We can see the device designed as a very simple and functional basic mechanism,

to which were added the accessory parts, such as transmissions and the setting

quadrilateral, to make it suitable to the required specifications. It presents some

improvable solutions for the proposed use or not needed in different situations. In

the future, we will check if the device characteristics match the patient's effective

needs, in which case we will continue with the improvement of the device up to

arrive at a real commercial product.

Chapter 5

74

Bibliography

[1] Duncan E Wood, JH Burridge, FM Van Wijck, C McFadden, RA Hitchcock,

AD Pandyan, A Haugh, JJ Salazar-Torres, and Ian D Swain. “Biomechanical

approaches applied to the lower and upper limb for the measurement of

spasticity: a systematic review of the literature”. Disability & Rehabilitation,

27(1-2):19-33. 2005.

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