A FLEXIBLE ROBOTIC SYSTEM FOR COMPLEX

STRUCTURE ASSEMBLY

By

Wenbo Sun

B.Sc., University of Science and Technology of China, 2018

Thesis

Submitted in partial fulfillment of the requirements for the

Degree of Master of Science in the School of Engineering at Brown University

PROVIDENCE, RHODE ISLAND

MAY 2020

ii

This thesis by Wenbo Sun is accepted in its present form by the School of Engineering

as satisfying the thesis requirements for the degree of Master of Science

Date______________ _________________________________

Haneesh Kesari, Advisor

Approved by the Graduate Council

Date_______________ _____________________________________

Andrew G. Campbell, Dean of the Graduate School

iii

ACKNOWLEDGEMENTS

First, I would like to thank my research advisor, Professor Haneesh Kesari, for providing me such a

wonderful opportunity to do research under his professional supervision. This thesis would not have

been possible without his guidance and encouragement. Moreover, in his class Advanced Mechanical

Engineering I learned rigid body kinematics which plays a key role in this project. In addition, I would

like to thank Professor R. Iris Bahar for her course Design of Robotic Systems, which equipped me with

the electronics theories and skills. This information was vital to my experiments. Then, I would like to

mention the other group members, Weilin Deng, Wenqiang Fang, and Sayaka Kochiyama, for their

kind assistance throughout this project. They are excellent researchers and warmhearted friends. Finally,

I should thank Mrs. Corrie Mook and my parents, who gave valuable revision suggestions for this

thesis.

iv

Table of Contents

Acknowledgements ................................................................................................................... iii

Table of Contents ....................................................................................................................... iv

List of Figures .............................................................................................................................. v

1 Introduction ........................................................................................................................ １

2 Robotic Assembly System and Synthesis Process ................................................... ３

2.1 Function Requirements of the System ........................................................................ ３

2.1.1 Identify the Polyhedron .......................................................................................... ３

2.1.2 Assemble the Composite ......................................................................................... ３

2.1.3 Bond Polyhedrons by Glue ..................................................................................... ３

2.2 Synthesis Process .......................................................................................................... ４

2.2.1 System Composition ............................................................................................... ４

2.2.2 Processing Steps ..................................................................................................... ４

3 Preliminary Experiments ............................................................................................... ７

3.1 Device Setup.................................................................................................................. ７

3.2 Assembly Task .............................................................................................................. ８

4 Stewart Platform’s Design and Manufacture ........................................................... ９

4.1 Introduction .................................................................................................................. ９

4.2 Design Principle and Manufacture Details ................................................................ ９

4.2.1 Platform Structure and Assembling ..................................................................... ９

4.2.2 Hardware Interface ......................................................................................... １０

4.2.3 Software Interface ........................................................................................... １２

4.3 Inverse Kinematics ................................................................................................... １３

4.3.1 Parameters of the Platform ............................................................................. １３

4.3.2 Inverse Kinematic Solution ............................................................................. １４

5 Conclusion ........................................................................................................................ １５

6 References ........................................................................................................................ １６

v

List of Figures

Figure 1.A The setup of the computer-vision assisted robotic assembly system............................. 4 Figure 1.B The positioner lays out the raw pieces from the storage on the platform...................... 4 Figure 1.C A computer-vision camera takes an image of the laid-out raw pieces on the platform,

which would be used for identifying the polyhedron with computer-vision algorithms......................................................................................................................

4 Figure 1.D The positioner picks up an identified, particular polyhedron that would be assembled

subsequently...................................................................................................................

4 Figure 1.E The positioner moves the polyhedron into the workspace of a delta-robot, which

prints glue onto the surface of the polyhedron...............................................................

4 Figure 1.F The glue-printed polyhedron is placed into its final configuration on the part being

constructed.....................................................................................................................

4 Figure 1.G The force applicator applies necessary force to the component as the glue

dries............ 4

Figure 2.A Some polyhedrons of typical materials that we propose to explore, including metal (steel and aluminum), polymer (PMMA), and ceramic (calcite)...................................

6

Figure 2.B The identified polyhedron shown in (A) using the computer-vision algorithms........ 6 Figure 2.C A four-axis robotic arm is assembling a hollow cylindrical structure with helix

patterns. The robotic arm picks hexagon tablets from the stack of tablets and place them as programmed to build the cylindrical structure..................................................

6 Figure 2.D Overall view of the constructed structure...................................................................... 6 Figure 2.E Side view of the constructed structure........................................................................... 6 Figure 2.F Top view of the constructed structure............................................................................ 6 Figure 3.A Overview of the Stewart Platform with a maze............................................................. 9 Figure 3.B Acrylic base and six 20 kg·cm servo motors installed on the base................................ 9 Figure 3.C Wooden foundation with three frame hanging strips..................................................... 9 Figure 3.D Acrylic payload platform connect with six fisheye carbon rod..................................... 9 Figure 3.E Acrylic maze’s bottom with anchor keys....................................................................... 9 Figure 4 Adafruit PCA9685 16-Channel Servo Driver circuit diagram.................................... 10 Figure 5 Timer 2 setup code...................................................................................................... 11 Figure 6 Interrupt function code................................................................................................ 11 Figure 7.A Definition of z-x-z sequence Euler angles.................................................................. 12 Figure 7.B Parameters of the Stewart Platform............................................................................ 12 Figure 7.C Relationship among servo arm, rod, and the distance between two joints................. 12

１

1 Introduction

Flexible robotic systems have been recognized as key to the futures of manufacturing, scientific

research, transportation, service, and entertainment1. These applications entail significant social and

economical impacts2,3. In factories, industrial robots are leaving their cages and working with human

workers cooperatively to combine a robot’s productivity and human’s flexibility in production lines4,5.

Meanwhile, in laboratories, highly flexible robotic systems are needed to produce large numbers of

diverse samples that are designed by researchers. For example, many material science and mechanics

experiments require a researcher to design and create hundreds or even thousands of samples in

different structures. Without an automated production line, it would require significant manpower,

which is the most precious resource in research groups.

Technically, it is challenging to design flexible robotic systems. Unlike traditional robotic systems that

work in deterministic conditions and unchanging process, flexible robotic systems need to operate in

highly stochastic conditions and changing process. That requires flexible robotic systems be equip with

rich senses, critical judgements, and multiple functions. Due to the complexity and diversity of the

requirements, flexible robotic systems should be designed for specific tasks. Therefore, focusing on our

laboratory’s pressing needs in experiments, this thesis proposes an automation solution for structure

assembly and glue, discusses the feasibility of the solution by experiment, and provide an improvement

plan to further increase the system’s flexibility.

In our research group, a robotic assembly system has been strongly needed. The preliminary

experiments and simulations of our group show that weak interfaces can enhance work of facture. The

failure of brittle materials primarily takes place by the growth of sharp cracks. Cracks grow relatively

easily if their tips are oriented in directions that are perpendicular to the direction of the applied

force6,7,8. The repeated arrest of propagating cracks and generation of new cracks can cause the fracture

of the solid to consume substantially more energy, thus effectively toughening it9,10. These statements

are supported by observations of remarkable toughness enhancements in stiff structural biological

materials (SSBMs), such as bones and shells. The researchers of our group found that the SSBMs can

be equivalent to a large assembly of tablets or bricks composed of a brittle material and stuck together

２

with weak bonds11,12. Inspired by the remarkable toughness enhancement mechanism of SSBMs, our

group plans to create a family of composites, SSBM-composites, which are assemblies of a large

number of “tablets.” The tablets in SSBM-composites we designed have relatively general shapes, so

we refer to them as “polyhedron.” They will be bonded together by glue and/or mechanical interlocking.

In order to translate the designs yielded by our optimization into physical parts and conduct mechanics

tests on them to verify whether the material structures we designed are indeed optimal, we need to

conduct a significant amount of experiment on SSBM-composites samples.

In the preliminary experiments, we laser cut the acrylic sheet into hundreds of pieces and glued them

up piece by piece with hands. To make one SSBM-composite sample requires over 20 hours of a

researecher, which is too time consuming for us to do a large number of experiments on a family of

composites. Therefore, we need to automation production line to make these samples for us. This

requires a highly flexibility of the robotic system that should be able to assemble various structures of

composites that consists of multiple scales and shapes of polyhedrons and be capable to glue the

polyhedrons up in many different ways.

The focus of this thesis is to propose an automation solution for our group’s further experiment

requirements on SSBM-composite. The design of the flexible robotic assembly system and the

corresponding synthetic process are discussed in chapter 2. The experiment based on a 4DOF robot arm

for testing the feasibility of the synthetic process is described in chapter 3. Finally, the manufacturing

and control methods of the Stewart Platform is shown in chapter 4, which can further increase the

system’s flexibility.

３

2 Robotic Assembly System and Synthesis Process

2.1 Function Requirements of the System

2.1.1 Identify the Polyhedron

The flexible robotic systems should be equipped with rich senses. In the system, the input material,

polyhedrons, will be cut from raw material sheets by cutting machines (e.g. laser cutter, wire cutting

machine, etc.) according to the blueprints designed by experimenters. After cutting, we generally get

dozens or hundreds of polyhedron whose scale is from millimeters to centimeters. In practice, it is

difficult to move the polyhedrons out of the cutting machines without breaking their original orders.

Therefore, in most cases, the input materials (polyhedrons) are disordered. This requires the robotic

system be able to identify the polyhedrons by their shapes, colors, or other artificial marks.

2.1.2 Assemble the Composite

Being different from the industrial production lines whose industrial robot is always repeating several

predetermined movements and dealing with a single type of objects, the robots in the flexibly robotic

assembly system should be able to pick up the object in multiple scales from millimeters to centimeters,

which means the weights and surfaces of the objects are generally significantly different among tasks.

Thus, the system should have multiple functions. That means the end of the manipulator need a highly

flexible grasping ability to adapt to objects in different shapes and sizes. Meanwhile, the assembly

tasks require the manipulator has high repeated precision, especially for the small scale structures’

assembly. Besides, the system should have critical judgements as well. Given that the input materials

are disordered and the structures are complex, the system should be capable to work out the optimal

assemble sequence.

2.1.3 Bond Polyhedrons by Glue

The interfaces are generally different in different composites’ structures. Most of the composites are in

crossed-layered architecture, which consists of several layers of staggered polyhedrons. Hence, the

４

robotic assembly system should be capable of putting glue on all sides and surfaces of the polyhedrons.

In addition, the bonding process of different kinds of glue all require a process of pressing the

polyhedrons together to eliminate any gaps. Many types of glue require additional steps, such as press

bonding, optical bonding or heating bonding.

2.2 Synthesis Process

2.2.1 System Composition

The robot assembly system consist of two 6DOF manipulator with force sensors and torque sensors, a

delta robot, a computer vision system with three cameras, and a turnable stage with lifting platform.

Because the system need to press force on polyhedrons, the two manipulators should have force and

torque senses to control their micro-movements in press process. The delta robot is capable of very fast

motion, so that using it as glue printer. The computer vision system can help the system identify the

input materials and monitor the assembly process. The turnable stage with lifting platform can expand

the work space of the system.

2.2.2 Processing Steps

S.1 Images of the polyhedrons will be continuously collected using three overhead cameras. The

cameras will be positioned and oriented such that all points in the workspace are in the scope of

at least two cameras. The images will be sent to a central computer workstation that will oversee

and direct the entire on the central workstation. The algorithms will make use of the shape, color,

and texture of the polyhedron to identify them. To ensure its proper position and orientation, the

algorithms will make use of the cameras’ focal lengths and compare the images of the

polyhedron with those of easily identifiable reference objects of known geometry, position, and

orientation that remain fixed during the synthesis process.

S.2 A 6DOF robotic manipulator will use vacuum suction and van der Waals adhesion to pick up the

polyhedron (Figure 1B). We refer to the 6DOF manipulator as the positioner. The positioner will

move the polyhedron into the work space of a delta robot (Figure 1E).

５

S.3 The end effector of the delta robot is an extrusion system that is capable of printing glue onto the

polyhedron at high speeds (≈5mm/s) (Figure 5E). We have explored different types of glues as

part of our preliminary research, including UV- and visible light-curable glues and heat curing

adhesives. Based on the air-drying glues start setting as soon as they are exposed to air, we

selected standard air-drying glues for the project. This is the reason behind us choosing a delta

robot to print the glue onto the polyhedron, instead of a regular robotic manipulator; for a given

spatial precision, a delta robot is capable of much faster motion that a regular robotic manipulator.

Therefore, the delta robot will allow us to print the glue fast enough so that when the polyhedron

is placed into its final configuration on the part being constructed, the glue is still uncured

enough to bond the polyhedron to the part.

Figure 1: (A) The setup of the computer-vision assisted robotic assembly system. (B) The positioner

(6DOF manipulator) lays out the raw pieces from the storage on the platform. (C) A computer-vision

camera takes an image of the laid-out raw pieces on the platform, which would be used for identifying

the polyhedron with computer-vision algorithms. (D) The positioner picks up an identified, particular

polyhedron that would be assembled subsequently. (E) The positioner moves the polyhedron into the

workspace of a delta-robot, which prints glue onto the surface of the polyhedron. (F) The glue-printed

polyhedron is placed into its final configuration on the part being constructed. (G) The force applicator

applies necessary force to the component as the glue dries. The models of 6DOF manipulator,

delta-robot, and lifting platform are modified based on the CAD files13, 14, 15.

６

S.4 After the glue is applied, the positioner will move the polyhedron to its final location on the part

being constructed (Figure 1F). A second 6DOF robotic manipulator will apply the necessary

force to the polyhedron as the glue dries (Figure 1G). We refer to this second manipulator as the

force applicator.

S.5 As the size of the structure being constructed grows, the turnable stage (shown in Figure 1A) will

be rotated and its height adjusted so that the region of the part where the next polyhedron is to be

placed is always within the workspace of both the positioner and the force applicator.

The position repeatability of the 6DOF robotic manipulators and the delta robot is 0.2mm. Based on the

size of laser beam spot, it is possible for us to create polyhedron whose dimensions are just a few

millimeters and whose geometry is accurate up to ±50 microns. Thus, our synthesis technique will be

able to approximate the geometry of a desired part with millimeter scale accuracy. In the preliminary

stage of the project, assembling a polyhedron by picking up, glue printing, placing it in the final

configuration, and holding it took a total time of 20-60 seconds (depending on the glue properties).

Therefore, typically, the robot-assisted assembly of a structure shown in Figure 2D, which contains 450

polyhedrons, would cost a total time of 2.5-7.5 hours.

７

3 Preliminary Experiments

In order to test the feasibility of the synthesis process, many experiments had been done, such as the

feasibility of identification, assembly, glue process, forcing process, and glue curing assistant process.

For testing feasibility of the assembly process proposed in last chapter, especially the manipulator’s

positioning accuracy and algorithm feasibility, we used a 4DOF manipulator to simulate the 6DOF

manipulator assembly process and minimized the costs of the preliminary experiment.

3.1 Device Setup

DOBOT Magician is a multifunctional desktop robotic arm. Its position repeatability is 0.2mm, which

has the same position repeatability of the 6DOF manipulator and the delta robot which mentioned in

the proposed robotic assembly system16. It has four degrees of freedom, which is good enough to

simulate most of the positioner’s independent functions, such as picking up and dropping down

polyhedrons, and assembling relatively complex structures. In order to assist the robotic arm to store

and locate the large number of the raw pieces, a storage case has been designed for it (shown in Figure

2C).

Figure 2: (A) Some polyhedrons of typical materials that we propose to explore, including metal (steel

and aluminum), polymer (PMMA), and ceramic (calcite). (B) The identified polyhedron shown in (A)

using the computer-vision algorithms. (C) A four-axis robotic arm is assembling a hollow cylindrical

structure with helix patterns. The robotic arm picks hexagon tablets from the stack of tablets and place

them as programmed to build the cylindrical structure. The (D) overall view, (E) side view, and (F) top

view of the constructed structure. The structure is composed of 450 hexagon tablets stacked in 75

layers.

８

In the experiment, the end effector is a 20mm (in diameter) vacuum suction cup. Its pressure maximum

is about -35 KPa. To pick up the pieces, the vacuum suctions air and holds the piece throughout the

movement. To drop the pieces, the vacuum pump must blow a small amount of air to stop the suction,

because the adhesion between the suction cup and the polyhedron will prevent the separation of the

polyhedron from the end effector.

3.2 Assembly Task

One objective of the assembly process testing experiments is to test the performance of the robotic arm

when they conduct assembly task. A hollow cylindrical structure with a helical pattern was designed

(shown in Figure 2D, 2E, 2F). In this structure, each layer has six hexagon tablets, and two adjacent

layers have an angle of deviation of 15 degree. By observing the repeated motion needed to construct

the cylindrical structure, we can easily estimate the position repeatability of the robotic arm. Hexagon

tablets were laser cut from 1/16 inch acrylic sheets with a diagonal distance of 25mm. Therefore, the

tablet is quite light. The adhesion between suction cup and the tablet cannot be ignored.

From the experiment results shown in Figures 2D, 2E, and 2F, we can determine that the robotic arm

can assemble the cylindrical structure with precision. This means, the position repeatability of the

robotic arm is good enough for our project, and the adhesion between the suction cup and tablets can be

overcome by programming the ability to blow air into the design of the vacuum pump.

９

4 Stewart Platform’s Design and Manufacture

4.1 Introduction

The Stewart Platform is the most celebrated 6DOF parallel manipulator, which consists of two rigid

bodies (referred to as the base and the platform) connected through six extensible legs, each with a

spherical joint at one end and a universal joint at the other, or with spherical joints at both ends17. It can

perform three dimensions of linear movements and three dimensions of angular movements18. The

platform was initially utilized in flight simulators for its unique advantage (better stiffness and precise

positioning capability) over conventional serial robots19. It’s also widely used as the movable platform

in many devices that require high precision such as large radio telescopes20.

In our original design of robotic assembly systems, the workspace is based on a turnable stage, which

has two degrees of freedom: one vertical translation degree of freedom and one rotation degree of

freedom. If we replace the 2DOF turnable platform by a 6DOF Strewart Platform, there would be a

significant increase in the flexibility of the robotic system.

4.2 Design Principle and Manufacture Details

The Stewart Platform system consists of a wooden foundation for system stabilization, an acrylic base,

an acrylic platform, six 20kg·cm servo motors, a controller system and an acrylic maze (shown in

Figure 2A).

4.2.1 Platform Structure and Assembling

The base of a Stewart Platform includes 3 parts: a bottom, stanchions, and a sub-platform (shown in

Figure 3C). The bottom layer is laser cut from a 1/4 inch acrylic sheet. Six servo motors and an electric

circuit are affixed to the top of the bottom layer. The back of the bottom layer is connected to the

wooden foundation using 3M picture hanging strips in order to fasten the whole system. Three

stanchions are made by metal posts and screws. They lift the sub-platform from the bottom layer. The

sub-platform is fixed on the top of the metal posts by screws. It is also laser cut from a 1/4 inch acrylic

１０

sheet. The holes on it are left for wires to go through. The frame hanging strip on top is used for

attaching Arduino board.

Figure 3: (A) Overview of the Stewart Platform with a maze. (B) Acrylic base and six 20 kg·cm servo

motors installed on the base. (C) Wooden foundation with three 3M picture frame hanging strips. (D)

Acrylic payload platform connected to six fisheye carbon rods. (E) Acrylic maze’s bottom with anchor

keys.

The Payload platform of the Stewart Platform is connected with six carbon rod by six spherical joints

(shown in Figure 3D). We glued four nuts in parallel on each connection of the payload platform so that

rods can be connected to the payload platform by screws. As shown in Figure 3D, there are four shaped

holes on the platform. They are connecting ports for functional units attached above. In this experiment

the maze is the functional unit.

4.2.2 Hardware Interface

The hardware interface consists of five functional parts: Arduino UNO, an Adafruit PCA9685

(16-channel servo driver), an analog joystick, two push buttons, and six DS3218 digital servos.

Arduino UNO is working as the core controller in the system. It is responsible for collecting sensor

information from the joystick and push buttons and then converting them to servo actuating outputs.

The Adafruit PCA9685 16-channel servo driver is used to actuate six servos at the bottom of the

platform. The driver can also be set up to light multiple LEDs. This I2C shown in Figure 4 is a perfect

１１

solution for projects that require a number of servos to work simultaneously. It can drive up to 16

servos, which only takes up 2 pins from Arduino. The two control pins connected to Arduino are SCL

and SDA. The SCL is connected to the Arduino clock line (A5) and the SDA is connected to the data

line (A4)21. The functional component of the driver is the PCA9685 chip in the middle of the board. It

contains an I2C bus controller and multiplexer which can distribute specific power to each of the servos

according to the signal received from Adruino through the SDA pin22. The servo drive I2C is powered

by the 5V Arduino power output through control pin Vcc. An external 12V power is also connected to

the supply for servo powering through pin V+ with a wall adapter. Since we are driving 6 servos at the

same time, the current draw among servos is estimated to be large. In order to prevent the negative

effect caused by this issue, a 1000μF capacitor should be soldered at the thru-hole capacitor slot. In

order to program the servo drive I2C, a pre-designed Arduino library <HCPCA9685.h>23 can be used.

Figure 4: Adafruit PCA9685 16-Channel Servo Driver circuit diagram

The analog joystick used in this project consists of two potentiometers mounted at a 90 degree angle.

Each potentiometer represents one direction. It is powered with 5V DC supplied by Arduino.

Depending on the position, the joystick will output 2 voltage readings --- VRx and VRy --- ranging

from 0-5V. The 2 voltage readings are then read by Arduino using the A0 and A1 pins. It is expected to

read the input position value between 0 ~ 1023, at around 512 at its resting position24. The two values

are then converted to servo actuating signals through the software interface.

１２

Six DS3218 digital servos are the actuators in the Stewart Platform. This type of servo has an operating

voltage range between 4.8V – 6.8V. Each servo is able to provide a torque up to 20 kg·cm. The pulse

width range is from 500-2500μsec with the neutral position at 1500μsec. The six servos are connected

to 6 output ports on the PCA9685 16-channel servo driver.

4.2.3 Software Interface

Using timer interrupt processes the signal input from joystick. We set Timer2 with an interval of 5ms.

The specific code for the Timer2 set up is shown in Figure 5. It takes the position from the joystick

every 5ms into the interrupt function. Inside interrupt, it averages 20 position inputs and then sends an

output to servos. As a result, from the servo side, each servo receives an on-position command every

100ms. The code for interrupt function is shown in Figure 6. Using interrupt slows down the position

input rate from the joystick, which enhances the synchronization the between servos and the joystick.

Figure 5: Timer 2 setup code

Figure 6: Interrupt function code

１３

4.3 Inverse Kinematics

4.3.1 Parameters of the Platform

The inverse kinematics of the Stewart Platform is to determine the position of the servo arm by giving

the pose of the payload platform. The payload platform can be regarded as a rigid body. Therefore, its

pose can be described as a vector with six components:

),,,,,( γβαzyxQ =

(1)

In pose vector, ）（ zyx ,, describes the position of the payload platform. It is the translation vector

from the initial position to the new position. The other three parameters are Euler angles, which

describe the orientation of the payload platform. We know that there are 12 sequence of Euler angles25.

In this project, we define the Euler angles in the z-x-z sequence (shown in Figure 7A).

Translating Euler angles to rotation matrix R:

−−+

−−−=

ββγγββαγαγβαγβααγβαγααγβγαβγα

cossincossinsinsincossinsincoscoscossincoscossincos

sinsinsincossincoscossinsincoscoscosR (2)

Figure 7: (A) Definition of z-x-z sequence Euler angles. (B) Parameters of the Stewart Platform.

(C) Relationship among servo arm, rod, and the distance between two joints.

The position of the six servo arm’s shaft is iA

, the position of six joints on the moving payload

platform is iB

, and the original position of the joints on the platform is 0iB

(shown in Figure 7B). The

１４

length of the servo arm and rod are R and L , respectively. The distance between the servo arm’s

shaft and the joint on the payload platform is l . The angle between R and il is iθ .

4.3.2 Inverse Kinematic Solution

The distance between the arm’s shaft and the joint on platform il is determined by given iA

, 0iB

and Q . The new position of the joints on platform iB can be calculated as:

tBRB ii

+= 0 (3)

where 0iB is the payload platform’s original position vector, R is the rotation matrix, and

),,( zyxt = is the translate vector. The distance between the arm’s shaft and the joint on the platform

is il .

iii ABl

−= (4)

iii lll

· = (5)

Then we calculate the servo’s angle change iθ . According to cosine law, we can derive the original

angle 0Θ and the moved angle iΘ of servo arms as:

LR

LRli

2arccos

2220

0−+

=Θ (6)

LR

LRli

2arccos

222 −+=Θ (7)

The angle change iθ is:

LR

LRlLR

LRl iii 2

arccos2

arccos-222

0222

0−+

−−+

=ΘΘ=θ (8)

Formula (8) is the inverse kinematic solution we need. Given platform pose iB , the controller can

derive the servo motors’ angle change iθ .

１５

5 Conclusion

In this thesis, a flexible robotic system was designed to assemble complex structures. A synthesis

process was also proposed based on the system. Given that we could not purchase all the devices we

listed in this design before we conform whole design is feasible, a family of simplified preliminary

experiments had been done for testing the feasibility of the synthesis process and the rationality of the

robotics system’s design. These experiments mainly tested the assembly performance of the

manipulator, which showed the robotic arm with 0.2 mm position repeatability could meet our

requirements and that the assembly process is feasible. However, we could not do experiments for the

process of applying glue, as we do not be equip with enough devices. Both of the two processes need

the cooperation between at least one 6DOF manipulator and one 4DOF manipulator. Finally, a Stewart

Platform was designed and manufactured to replace the turnable stage in the original design of the

robotic system to further increase the robotic system’s flexibility.

Future work could further test and improve this robotic assembly system and synthesis process by

using 6DOF manipulators and delta robots. There is good reasons to believe that this kind of

flexible assembly robotic system will greatly advance development of mechanics and material

science.

１６

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12. Monn, Michael A., James C. Weaver, Tianyang Zhang, Joanna Aizenberg, and Haneesh Kesari.

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4976-4981.

13. Universal robot-UR5 robot.

１７

http://www.traceparts.com/en/search/universalrobots?CatalogPath=UNIVERSAL_ROBOT

%3AF_UNIVERSAL_ROBOTS.

14. Delta robot.

https://grabcad.com/library/delta-robot-6-axis-packaging-assembly-m-1ia-0-5a-1

15. Hydraulic scissor lifting platform. https://gradcad.com/library/hydraulic-scissor-lifting-platform-1

16. Dobot Magician Specifications https://www.dobot.cc/dobot-magician/specification.html

17. Dasgupta, Bhaskar, and T. S. Mruthyunjaya. "The Stewart platform manipulator: a

review." Mechanism and machine theory 35, no. 1 (2000): 15-40.

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mechanical engineers 180, no. 1 (1965): 371-386.

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USA, 1978.

20. Yanhui, Jia, Li Jianjun, and Wang Yuzhe. "Structural Analysis and Data Processing of Feed Cabin in

Large Radio Telescop." Machinery 9 (2014): 6.

21. Adafruit PCA9685 16-Channel Servo Driver datasheet, Bill Earl

https://learn.adafruit.com/16-channel-pwm-servo-driver?view=all#using-the-adafruit-library

22. PCA9685 16-channel, 12-bit PWM Fm+ I2C-bus LED controller Rev. 4 — 16 April 2015

Product datasheet. https://cdn-shop.adafruit.com/datasheets/PCA9685.pdf

23. HCPCA9685 - Library for PCA9685 16ch 12bit PWM controller

https://forum.hobbycomponents.com/viewtopic.php?f=58&t=2034#p4956

24. Joystick Module Datasheet. http://www.energiazero.org/arduino_sensori/joystick_module.pdf

25. Harib, K., and K. Srinivasan. "Kinematic and dynamic analysis of Stewart platform-based machine

tool structures." Robotica 21, no. 5 (2003): 541.