multi-delta robotic arm modeling project report

Multi-Delta Robotic Arm

Michael Ache

Allen Joseph

Sean Treiber

Uduak Udongwo

EML 4024C

Spring 2015

Midterm Project

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Introduction

The objective of this project is to fully model and analyze a multi-delta robotic arm with

a functioning claw attachment. Delta robotic arms have many uses in fields such as palletizing,

3-D printing and laser sintering. The multi-delta arm consists of platforms and rods connected by

ball joints. The motion of the arm is controlled by three rotational motors located at the base of

the arm. These motors control the rotation of the initial connecting arms. This rotational motion

is then transferred to the sequential connecting arms and platforms through the rods and ball

joints. This allows the entire arm to be controlled through the timing of the three motors. The

multi delta arm ideally can revolve about is central axis as well as being able to extend and

collapse along this central axis. In order to fully model this arm a triple delta configuration was

selected and the claw was modeled from the claw utilized in a toy crane machine. The parts first

designed were the rods and ball socket joints which make up a majority of the arm. Next the

connecting arms, and delta platforms were designed as well as the base and the claw parts. The

mechanical design section details the procedures used to create all parts, subassemblies and then

the final assembly. The exploded view should all of the parts of the triple delta configuration

separated out from the central assembly can be found in the mechanical design section. During

the mechanical design phase, materials were selected for each of the parts in the triple delta

configuration. The mass properties were then calculated and recorded. These values can be found

in the table in the mass properties section. In addition to this table an analysis of the chosen

materials is included and details the consequences of these design decisions. In order to

calculate the motion study and motion analysis, the model was simplified to a double delta

configuration. This was done do to the fact that the triple delta configuration is too

computationally intensive to be able to achieve the motion required by this project. The

mechanism kinematics section delineates the details and results of this motion analysis.

Mechanical Design

Base Design

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Main Base Plate

The first geometry of the base was sketched as a 2-D

drawing on the top plane. Here, a lot of centerlines and

geometric constraints were used in order to create the

equilateral structure. The centerlines also were used to

provide a reference to make key angles in the design. Some

of the key constraints and dimensions were perpendicular

constraints, 60 degree angular dimensions for the inner

triangle, and parallel lines between the top of each fin and

the corresponding triangle line segment. The three linear

dimensions given in the sketch were 3.5” for the inner

triangle length, 0.75” for the top of the fins displacement

from the inner lines of the triangle, and 0.40” along the top

of each fin. After the sketch was completed, the plate was

extruded (with the blind option) by 0.20”.

Figure 1: Base Plate Sketch

Figure 2: Base Plate Extrude

Next, sketches were made on the top of the base plate on

plane x-z. These sketches were 3 parallelograms that mainly

consisted of parallel constraints to the edges of the base

plate. The sketch was also dimensioned relatively close to

the corners of the base plate in order to provide support to

the motors that will be shown later. The separation of the

line segments of the parallelogram to its parallel corner

segment was 0.02” and the parallelogram had a length of 1”.

Next, the sketch was extrude upwards by 2.5”.

Figure 3: Parallelogram Sketch

Figure 4: Parallelogram Extrude

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The rigs were then cut by drawing up a funnel-shaped

sketch on the face of the rig. The middle of the sketch was

then dimensioned at a length of 1.36” separation from the

top face of the base plate. Next, an extrusion cut was used

to take out the unnecessary pieces of the fin. Since the fin

had a parallelogram cross-section, the each fin still had

excess side pieces. A cut-extrude was used on these pieces

at 0.03”. All three fins were cut to form this geometry.

Figure 5: Rig Sketch

Figure 6: Rig Cut 1

Here, a rectangular prism is extruded on the top of the fin.

This piece is the critical point of contact for the motor

assembly onto the base. A rectangular sketch was created

with a length extended along the fin’s length and a width of

0.25”. The sketch was then extruded 0.25”. Each fin had the

same rectangular prism on the top and dimensioned the

same way.

Figure 7: Rectangular Prism

Sketch and Extrude

The motor attachment hole was created as a circular sketch at

the closer side of the prism to the edge of the fin. A set

diameter of 0.10” was assigned to the circle. The placement

of the circle was on the center of the rectangular prism cross-

section. After the sketch specifications were created, the

sketch was then extruded through the material in order to cut

off the cross section through the prism. This hole is the joint

Figure 8: Sketch on

Rectangular Prism

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where the fasteners will secure the motors

Figure 9: Extrude on

Rectangular Prism

The completed main base will be used as the foundation of

the triple delta robotic arm. Therefore this part of the base is

designed to be a rigid structure that can support the loadings

of the arms and the claw. This part of the entire base sub-

assembly was scaled up at a factor of 20/3 in order meet the

size requirements of the rest of the robotic arm assembly

Figure 10: Main Base

Complete

The main motor cross section was sketched on the top X-

Z plane. The length of the motor was 1.5” and the width

was 0.75”. The center of the rectangular is fixed to the

origin of the plane. Also, 2D fillets of 0.05” were added

on the corners for a better aesthetic appearance. Then, the

sketch was extruded at a depth of 2”. Then, fillets were

added to the top and bottom cross section of the motor at

the same dimension as the 2D fillets. These fillet

additions further enhanced the overall motor appearance

by alleviating any sharp edges.

Figure 11: Motor Main Sketch

Figure 12: Motor Main Extrude

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Figure 13: Motor Fillet

Next, the motor arm attachment hole was sketched along

the front X-Y plane of the graphics window right on the

parallel face of the motor. The hole was dimensioned at a

displacement of 0.50” up from the corresponding CSYS,

and the hole has a diameter of 0.15”. Next, a cut extrude

was applied to the inner motor surface at a depth of 0.50”

in the motor body. A third of the overall length of the

motor was chosen for the cut depth in order to ensure the

security of the rod attachment onto the motor arm.

Figure 14: Motor Hole Sketch

Figure 15: Motor Hole Extrude

On the top of the motor, which is on the X-Z plane, a

rectangular sketch was formed close to the front edge of

the motor. The rectangle was displaced at 0.18” from the

edge line of the motor top. A vertical centerline was

created at the vertical center of the plane in order to

center the sketch along the z-axis. The dimensions of the

rectangle were 0.10” wide and 0.38” long. Afterwards, Figure 16: Motor top Sketch

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the rectangle was extrude at a height of 0.25” high.

Figure 17: Motor top Extrude

A circular sketch was then formed on the front face of the

rectangular top fin. This sketch was in the center of the

front face of the fin. The diameter of the circle is 0.10”.

Next, the hole was extruded through the fin. The fin of the

motor will be fastened onto the main base model with this

hole.

Figure 18: Motor Top Hole

Sketch

Figure 19: Motor Top Hole

Extrude

Fillets were applied on the rectangular fin at the corners.

The first fillet was located at the linear edges of the

rectangular fin and the radius dimension was 0.175”.

Next, a second fillet was inserted at the bottom back edge

of the motor fin. The radius of this fillet was 0.045”.

These fillets created a realistic edge blend on the fin of the

motor. Figure 20: Motor Top Fillet

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Figure 21: Motor Top Fillet 2

The final motor is shown on the right. The completed

motor is a simple geometric figure, but is very vital in the

motion of the whole robotic arm. In the real world, this

motor triggers the power and energy to ignite motion in

the arms of the robot. The motor was another part in the

final base sub-assembly that was scaled up by a factor of

20/3. This means that all the sketches and extrudes

involved in the final product were scaled by this factor. Figure 22: Completed Motor

The hex bolt head was sketched as a patterned polygon of

6 sides, with a circumscribed circle along the line

endpoints of each line segment of the polygon. After the

sketch was complete, the head was extruded at a distance

of 0.125”.

Figure 23: Bolt Head Sketch

Figure 24: Bolt Head Extrude

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Next, a circular sketch was formed on the right Z-Y plane

on the hexagon bolt head. The diameter of the circle was

0.10”. Once the sketch was complete, it was extruded at a

depth of 0.60”. This depth was chosen to account for the

lengths of the side base rectangular prism, the motor fin,

the washer, and the nut.

Figure 25: Bolt Shaft Sketch

Figure 26: Bolt Shaft Extrude

A rectangular sketch was inserted on the top of the hexagon

bolt head. A centerline was sketched in order to center the

rectangle at the center of the bolt head. The rectangle was

assigned a width of 0.03”. After the sketch was fully

defined, then a cut-extrude of 0.025” was applied along

thickness of the bolt head. The purpose of this cut-extrude

is to create a screw point where the bolt can both get

loosened and tightened.

Figure 27: Bolt Head Cut Sketch

Figure 28: Cut Extrude at Bolt

Head

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The final hexagon bolt was designed to fasten the motor

onto the main base part. The shaft of the bolt has a diameter

that is consistent with the rest of the components in the

joint assembly (0.10”). The bolt was also scaled up by a

factor of 20/3.

Figure 29: Final Hex Bolt

The nut sketch was another 6-side polygon with a diameter

of 0.25”. The nut was then extruded at a depth of 0.125”.

Then a circular sketch was created on the y-x face of the

bolt with a diameter of 0.10”. This part could have been

developed without the cut-extrude feature. Instead, both the

polygon and the circle sketch could have been formed

initially before the first extrude. When extruding these

sketch, only the closed region that is selected will get

extruded.

Figure 30: Nut Sketch and

Extrude

The nut is important in the assembly because it will be used

to counteract and tighten the bolt connection to the base and

the motor. The nut, like the other components of the base

sub-assembly, was scaled by a factor of 20/3.

Figure 31: Final Nut

The washer was made basically as a sketch of a ring (an

inner and outer circle). The diameter of the inner circle was

0.10”, and the diameter of the outer circle was 0.20”. Then,

the section between the inner and outer lines of the washer

was extruded by 0.005”.

Figure 32: Washer Sketch and

Extrude

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The importance of the washer is that it behaves as a preload

that maintains the tension in an assembly where some slack

may be present. This washer will eliminate any rattling

effects that can occur within the motor joint assembly. This

washer is also scaled up by a factor of 20/3.

Figure 33: Final Washer

The rod piece was sketched as a simple circle with a

diameter of 1”. Then, the circle was extruded by 43/3”.

Figure 34: Rod Sketch and

Extrude

The rod piece was initially assigned a 1” diameter to

account for the rest of the assembly. The rest of the

components of the base had to get scaled up by 20/3 to get

the bottom motor hole to fit the rod. This attachment is

critical for the motion of the whole final assembly.

Figure 35: Final Rod

Figure 36: Scale Parameters

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Claw Design

Covering Cylinder

The first component in designing a functioning claw was

the central cylinder designated by the name covering

cylinder because it covers the driving pin. This part was

created by first doing a 2-D sketch along a vertical axis on

the front plane. This sketch was dimensioned and then

revolved about that vertical axis creating the cylindrical

shape. As shown in Figure 37.

Next, the 0.25 inch holes for the retaining hex bolts were

cut extruded into the top face a depth of 0.75 inches. The

next step was to extrude cut the central hole for the driving

pin, which was done through all.

A tangential plane was created, a rectangle was extruded

normal to the plane 0.75 inches in both direction 1 and 2,

then filleted with a radius of 0.5 inches and a hole was

extrude cut to accommodate a 0.25 inch hex bolt. These

features were circularly patterned three times equally

spaced, using the top edge of the cylinder as the parameter.

This will be used to secure the arm links to this covering

cylinder. As viewed in Figure 38.

Final Part is shown in Figure 39.

Figure 37: The covering

cylinder sketch.

Figure 38: The tangential

plane and subsequent

extrude

Figure 39: Covering

Cylinder.

Driving Pin with Triangular Base

The first step taking to create this component was to

extrude a cylinder with a diameter of 0.6 inches followed

by the extrusion of a circumscribed triangle with a

diameter of 4.75 inches. The cylinder was extruded to a

depth of 4 inches and the triangle was extruded 0.7 inches.

The next step in creating the driving pin was to extrude cut

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the slots for the claw fingers as well as creating the holes

for the linking hex bolts. The sketch for the claw finger

slot was circularly patterned to align with the three points

of the triangle and allowed for a claw finger with a

thickness of 0.5 inches. This step is shown in Figure 40.

Next, a plane was created mid-way between the inner faces

of the slots. This was used to extrude cut the 0.25 inch

holes needed to accommodate the linking bolt connecting

the claw finger to the triangular base of this driving pin.

This extrude cut was done through all and then circularly

patterned three times equally spaced using the top edge of

the cylinder as the parameter. This is displayed in Figure

41.

Countersinks were extrude cut 0.019 inches into the side of

the triangular base to allow for the use of hex bolts and

nuts. To do this another plane was created offset from the

mid plane created in the previous step and a circle was

sketched it with a diameter of 0.52 inches, which is equal

to the diameter of the head of a standard hex bolt with a

0.25 inch bolt diameter.

Final Part shown in Figure 42.

Figure 40: The extrude cut

sketch pattern.

Figure 41: Showing the

mid-plane and linking bolt

holes.

Figure 42: Driving pin with

Triangular base.

Claw Finger

This component was created by extruding a 2D sketch 0.25

inches. The sketch was created using the spline sketch tool

coupled with a tangential arc and four straight parallel

lines. The holes were made to accommodate the 0.25 inch

linking hex bolts. The distance between the holes was

established to be 2 inches. This Sketch is shown in Figure

43.

Figure 43: Claw Finger

sketch.

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The finish the component filets with all with a radius of

0.1 inches were added to the top surface and the curved

inner surface. In addition to these filets, a chamfer was

added to the leading edge of the claw finger, 0.2 inches at

an angle of 45 degrees.

Final Part is shown in Figure 44.

Figure 44: Claw Finger.

Claw Mounting Platform

The claw mounting platform was made by first sketching

an inscribed hexagon with a diameter of 20 inches, this

was followed by the creation of a central circle and a

circularly patterned set of lines constrained by the central

circle and the inscribed hexagon. This circular pattern used

the central circle as the parameter, and equal spacing

between instances. The dimensions given to the sketch

ensure that the piece matches the delta arm platforms on

the arm portion of the overall assembly. A circle equal in

diameter to the driving pin was also added to the center of

the sketch. This sketch was extruded 2 inches. This is

displayed in Figure 45.

The next step was creating the holes for the ball joints, this

was done utilizing a circular sketch which was mirrored

about the axis of symmetry and then circularly patterned

using the central circle as the parameter. This was

followed by an extruded circle in the center of each of

these cuts. The cut extrude was a depth of 0.55 inches and

the center circles were extruded to a thickness of 0.25

inches.

The next step was to extrude cut the holes for the bolts that

will retain the claw to the platform. These holes were cut

through all and were given a diameter of 0.25. This

component was finished with chamfers along the bottom

edge, 1.1 inches at 45 degrees. This is shown in Figure 46.

Final part is shown in Figure 47.

Figure 45: The base

platform sketch for

extrusion.


chamfered edges and the

ball joints locations.

Figure 47: The claw

mounting platform.

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Arm Link

This integral component was created using a straight shot

sketch with a length of 3.72 inches which was the length

required to have the claw fingers close when the driving

pin was fully retracted. The two holes were created to

allow for the use of 0.25 inch hex bolts and nuts. The

sketch was extruded 0.2 inches.

The final part is displayed in Figure 48.

Figure 48. The Arm Link.

Arm Design

Arm Platform The Arm Platform is where all Ball Joint Sockets and

Bearing Mount-to-Platform will mounted to. This acts

as the movable structure for the arm. It starts by

sketching a “T” inside an inscribed hexagon of a

diameter of 20 in. and a 2.0 in. thick flange on the “T”.

Making a circular pattern of 3 where the “T” webs will

intersect each other at the base circle of 3 in. was done

by creating 2 construction lines from the center and

coincide ting with the base of the “T” webs and

dimensioning an angle between them at 120 degrees.

This step is crucial since it defined the design intent of

making a delta robot arm. This is all shown in Figure

49.

The arm platform sketch was then extruded 2.0 in. as

shown in Figure 50. This dimension was chosen for the

extrusion to make it equal to the flange thickness of 2.0

Figure 49: Arm platform sketch

Figure 50: Arm platform extruded

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in.

A new sketch for the holes (each 1.5 in. diameter) were

made on the top face of the “T” flange by mirroring

and circular patterning followed by Extrude Cut of 0.55

in. deep shown in Figure 51. It is important to note that

the distance of the pairs of holes separated by a gap on

this platform must be measured and compared to with

the distance of the pair of holes at the end of the delta

arm in order for the rods that bridge the platforms are

parallel.

Pegs were then sketched at the bottom face of the holes

(each 0.5 in. diameter) and extruded 0.25 in. upward

shown in Figure 52. These pegs will be fitted into the

same diameter holes on the Ball Joint Sockets shown in

Figure 66 on page 19.

Another hole (0.75 in. diameter) was sketched at the

center on the side of the “T” flange for the Bearing

Mount-to-Platform Bolts which will hold the Bearing

Mount that will house the Bearings. It was an extrude

cut of 0.5 in as shown in Figure 53.

The next step was to mirroring the Extrude Cut feature

on the side of the “T” flange across the right plane.

This is shown in Figure 54.

The final step was to Circular Pattern in order to put

the mirrored and original Extrude Cut feature on the

side of all “T” flange. This is shown in Figure 55.

The completed part can be shown on Figure 56. Each

Arm Platform will have a total of 6 placements for the

each Ball Joint Socket that will sit on the top face of

the platform, and 6 holes for each bolt that will hold the

Bearing Mount-to-Platform. These parts will be discuss

in further detail in the next few pages.

Figure 51: Holes mirrored and

circular patterned

Figure 52: Sketch of pegs in holes

then extrude

Figure 53:Hole on side of flange

Figure 54: Mirroring holes about

right plane

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Figure 55: Circular Patterning the

holes on “T” flange side

Figure 56: The Arm Platform

Ball Joint

The Ball Joint is the fundamental component that

allows motion for the delta robot arm to be possible. It

was first created by sketching a semicircle using a

centerline through the origin, then using 3-point arc

tool starting from the origin to a reasonable distance

away on the centerline, and making the 180 degree arc

on the other side of the centerline. The diameter of the

semicircle was 2.0 in. The Revolving feature was used

to create a sphere by revolving the semicircle about the

Figure 57: Revolving the semi-circle

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centerline. This is shown in Figure 57.

A plane was created using the Reference Geometry

feature on the surface of the Ball Joint. The plane was

made tangent to the face of the sphere and then parallel

to the front plane (in this case). This is shown in Figure

58. This plane will be used as the sketch plane in the

next step.

On the new sketch plane, a circle of 1.0 in. was

constructed with the center being the point tangent to

the face of the sphere. This circle was then Extrude Cut

inward into the sphere at a depth of 1.0 in... This is

shown in Figure 59. This will create a hole for the rod

of the same diameter to be insert in to.

The completed Ball Joint can be shown in Figure 60.

The integral part will be assembled later with the Ball

Joint Socket and will allow the Ball Joint 3 degrees of

rotation.

Figure 58: Creating a plane

Figure 59: Extrude Cut a hole

Figure 60: The Ball Joint

Ball Joint Socket

The Ball Joint Socket was made for the purpose of the

Ball Joint to rotate freely with all degrees of rotation.

It’s created by using the sphere made in the Ball Joint

as a template as shown in Figure 57. The sphere is then

Shelled outward of a thickness of 0.1 in. This is shown

in Figure 61.

A new sketch is then made on one of the given planes;

in this case the right plane was chosen. A center point

Figure 61: Section view to display

Shelling

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rectangle was constructed with the given constraints:

one edge of the rectangle tangent to the edge of the

sphere and two corners coincident to the edge of the

sphere as shown in Figure 62. This ensures that if the

sphere were change in dimension, the rectangle

dimensions will change with it and maintain that

similar shape. An important dimension to note about in

this sketch is the 0.25 in. offset of the rectangle edge

from the origin. This dimension will govern the

limiting angle the Ball Joint can rotate within this part

without the rod interfering with this part during the

motion study.

Then the rectangle was used as the shape to Extrude

Cut with. Both directions and though all was chosen to

complete the Extrude Cut. This is shown in Figure 63.

The Extrude Cut was made for the Ball Joint to sit in

the cavity of the Ball Joint Socket.

A plane was then constructed similar to the one made

for the Ball Joint except this time the plane had to be

parallel to the face of the newly extruded cut socket. In

this case, the front plane happened to be the plane to

make that parallel reference since the front plane was

parallel to the shelled wall of the socket. This is shown

in Figure 64.

On this new plane, a circle of a diameter of 1.5 in. was

created with the center being at the point tangent to the

sphere surface. The circle is then extruded in two

directions: the first direction was to extrude up to the

body of the socket to ensure that the extrusion doesn’t

protrude into the inside wall of the socket, and the

second direction was to extrude 0.3 in. in the opposite

direction of the first. This is shown in Figure 65. This

will create the base for the socket to mount on the top

face holes of the Arm Platform.

Lastly, a hole is created from the face of the extrude

base by sketching a circle with a diameter of 0.50 in.

and centered on the face of that extruded base. The

circle is extrude cut of a depth of 0.25 in. This is shown

in Figure 66. This hole will be where the peg on the

Arm Platform will sit in.

Figure 62: Rectangle made for

Extrude Cut

Figure 63: Extrude Cut in both

directions

Figure 64: Creating a sketch plane

Figure 65: A base mount extrusion

for the socket

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The completed Ball Joint Socket in shown in Figure 67.

Figure 66: Extrude cut

Figure 67: Ball Joint Socket

Bearing Mount to Platform

The Bearing Mount to Platform was made to house the

Bearing with the Delta Connecting Rod. It was first

created by sketching a circle of a diameter of 1.0 in.

with the center at the origin on the front plane. Then a

new sketch is created on the top plane to draw a 3-point

arc with the center at the edge of the circle, the radius

of 1.0 in. at the center of the circle, and the angle of the

arc being 60 degrees as shown in Figure 68. The

importance of making the arc angle 60 degrees is to

ensure that the Delta Connecting Rods are aligned

which can be shown on page 24 Figure 80.

Figure 68: Sketch to Sweep

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The next step was to Sweep the circle along the 60

degree arc. This is shown in Figure 69.

After the Sweep, a new sketch was made on the end of

the swept face. A circle was made to match the face

and then Extruded 1.0 in. This is shown in Figure 70.

The extrusion was needed in order to provide a hole to

house the Bearing which the Delta Connecting Rod

will rotate.

The Bearing housing hole was then created by making

a new sketch on the extruded face. A circle centered on

the extruded face with a diameter of 0.75 in. was made,

and then extrude cut at a depth of 0.75 in. This is

shown in Figure 71. It is important to note that this hole

must not exceed a certain depth since another hole will

be created in the next steps, and holes cannot interfere

with each other.

A new plane is made by referencing the face from the

first sketch and setting the distance to be 2.05 in. This

is shown in Figure 72. This plane will be the sketch for

the hole for the Bearing Mount to Platform Bolt.

This new plane will be used as a limit to make a hole.

The feature Hole Wizard was chosen and used the

legacy hole to fully create this feature. The diameter of

the hole was made to be 0.75 in. to match the hole on

the side of the “T” flange on the Arm Platform.

This is shown in Figure 73. The completed Bearing Mount to Platform is shown in

Figure 74.

Figure 69: Swept circle sketch

Figure 70: Extruded face

Figure 71: Bearing housing Hole

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Figure 72: Creating plane

Figure 73: Sketch for hole using

Legacy Hole

Figure 74: The Bearing Mount to

Platform

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Bearing Mount to Platform Bolt

The Bolt was made with similar dimensions to the hole

made in the last step of the Bearing Mount to Platform.

The sketch then Revolved producing the bulk of the

Bolt. Dimension can be shown in Figure 75.

A new sketch was made on the Bolt head where a slot

was made for a screwdriver can be utilized. This is

shown in Figure 76.

The completed Bearing Mount to Platform Bolt is

shown in Figure 77.

Figure 75: Sketch and Revolve Bolt

Figure 76: Slot sketch and extruded

Figure 77: Bearing Mount to

Platform Bolt

Rod

The rod is the connection between the ball joints. They

allow forces to be transferred between components.

The rod was created from an extrusion of a sketched

circle. The Rod is shown in Figure ##.

Figure 78: Rod

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Bearing

The Bearing is the connection between the Delta

Connecting Rod and the Bearing to Platform Mount.

This bearing will allow rotation but not translation

between the rod and platform. The bearing was created

by Extruding a sketch of two circles on the sketch

plane. This component was created in class but the

radius has been modified from the one created in class.

The bearing can be seen in Figure ##.

Figure 79: Bearing

Delta Connecting Rod

The Delta Connecting Rod is the connection between

the Bearing and the Delta Arm. This is a direct

connection between the arm and the connecting rod.

Allows for rotation about the bearing in the platform.

The bearing was created by extruding on the sketch

plane for the main portion of the cylinder. Another

extrude was then created at each flat end of the rod and

extruded to the proper dimension. The Delta

Connecting Rod can be seen in Figure ##. Figure 80: Delta Connecting Rod

Delta Arm

The Delta Arm connects directly to the Delta

Connecting Rod and transfers rotation about the

Connecting Rod to translation through the Ball Joint

Socket connection. The Delta Arm was created by

extruding on the sketch plane. Extrude Cuts were then

performed on the proper planes to create the arm, hole

for the connecting rod, and connections for the ball

joint sockets. An extrude was performed on the base of

the ball joint sockets to create the second alignment

pin. The Delta Arm can be seen in Figure ## for the

Bottom and Figure ## for the Top Isometric View

Figure

81: Delta Arm (Bottom)

Figure 82: Delta Arm (TOP)

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Bottom Delta Arm

The Bottom Delta Arm has the same principles as the

Delta Arm, only change that has been made was the

removal of the third center Ball Joint Socket

connection on the bottom of the arm. The completed

arm can be seen in Figure ##.

Figure 83: Bottom Delta Arm

(Bottom)

Driving Delta Arm

The Driving Delta Arm connects directly to the Motor

and transfers rotation about the Motor Rod to

translation through the Ball Joint Socket connection.

The Driving Delta Arm was created by extruding on

the sketch plane. Extrude Cuts were then performed on

the proper planes to create the arm, hole for the

connecting rod, and connections for the ball joint

sockets. An extrude was performed on the base of the

ball joint sockets to create the second alignment pin for

the Ball Joint Socket connections. The Driving Delta

Arm can be seen in Figure ## for the Bottom and

Figure ## for the Top Isometric View

Figure 84: Driving Delta Arm (Top)

Figure 85: Driving Delta Arm

(Bottom)

Subassemblies

Ball and Socket Joint

The Ball and Socket Joint sub assembly was created by mating

the spherical of the ball to the socket wall. This part was then

saved and used in the connection of the Rod and Joint

Assembly. An important constraint was made on this

subassembly called limiting angles which only allowed the

Ball Joint to rotate where the Rod will not cross or interfere

with the Ball Joint Socket.

Figure 86: Ball and Socket

Joint

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Rod Sub Assembly

The Rod Sub Assembly was created mating the face of the end

of the rod to the inner face of the Ball surface. A Concentric

mate was used to align the rod surface with the inner spherical

surface of the Ball.

Figure 87: Rod and Ball

mates

The same steps were duplicated on the opposite side of the rod

in order to complete our Rod Sub Assembly.

Figure 88:Rod Sub Assembly

Bearing Mount Platform Sub Assembly

The Bearing Mount was mated using concentric of the bolt

hole to that of the platform hole that matched. The faces were

mated and rotation was restricted by aligning the planes of the

two components.

Figure 89: Bearing Mount and

Platform Mates

The bolt was then added to the sub assembly and mated

concentrically with the hole. The face of the bolt head was

mated to that of the bearing mounts matching hole. The plane

was then aligned with that of the Bearing Mount.

Figure 90: Bolt added to

assembly

26

The mated configuration was the reflected across a plane to

match the opposite face.

Figure 91: Reflection Plane

The two completed mated configurations were then duplicated

using a circular pattern about the center of the sub assembly.

This procedure was justified due to the fact that the mounted

components are not moving components.

Figure 92: Circular Pattern

Bottom Delta Arm and Connecting Rod Sub Assembly

The Connecting Rod Sub Assembly was started by taking the

Delta Connecting Rod and the Bearing and mating them

concentrically and with the appropriate faces. The same

procedure was completed on the opposite side of the Rod.

Figure 93: Bearing to Rod

mates

The Delta Arm is added. The Delta Arm valley is mated

concentrically with the outer spherical surface of the Rod. The

Planes are also mated to that the Rod doesn’t translate in the

arm valley.

Figure 94: Delta Arm to Rod

Mates

27

The Planes of the Rod and Delta Arm are mated. The Delta

Arm and Connecting Rod Sub Assembly is complete.

Figure 95: Plane Mate

Delta Sub Assembly

The bearing from the Delta Arm and Connecting Rod Sub

Assembly is added and mated to the Platform Sub Assembly.

The Bearing is mated concentrically with the hole of the

platform bearing mount and the face of the rod is mated with

the face of the mounting bracket.

Figure 96: Bearing to

Platform Bearing Mount Mate

The Rod Sub Assembly was added and mated with the face of

the socket to the inner face of the arm. Also mated

concentrically with the arm connection hole. This step was

repeated for the other connection holes in the Delta Arm.

Figure 97: Rod Sub Assembly

to Delta Arm Mate

The Bottom Delta Sub Assembly is now complete.

Figure 98: Bottom Delta Sub

Assembly

28

Middle Delta Sub Assembly

The steps for the Middle Delta Sub Assembly are the same as

that of The Bottom Delta Sub Assembly with one more rod

added to the third connection hole of the Delta Arm.

Figure 99: Middle Delta Sub

Assembly

Top Delta Sub Assembly

The Driving Delta Arm is added to the Sub Assembly. The

Rod Sub Assembly is then added and mated concentrically

with the connection hole of the driving arm. The ball joint

socket face is mated with the inner face of the connection

hole.

Figure 100: Driving Delta

Arm

The Rod Sub Assembly is added with the same procedure for

the other connection holes for the Driving Delta Arm. The

Top Delta is now complete.

Figure 101: The Rod sub

assembly

29

The Top Delta, Middle Delta, and Bottom Delta are finally

complete. They are now assembled by mating the appropriate

Rod Socket face to the appropriate Arm Hole using concentric

and coincident mates.

Figure 102: Mates between

the Platform sub assembly

and the connecting rods and

ball and socket joints.

Final Delta Sub Assembly

This is the Final Delta Sub Assembly completed.

Figure 103: Final delta Sub

assembly

Covering cylinder and Driving Pin The claw assembly started with the insertion of the Covering

cylinder. The driving pin was then inserted and mated

concentrically between the pin of the driving pin and the

covering cylinder slot. Also the distance between the bottom

of the covering cylinder and the driving pin was constrained.

These mates are shown in Figure 104.

Figure 104: The concentric

and limiting distance mates

between the Driving Pin and

Covering Cylinder.

30

Arm Links, Driving Pin and Covering Cylinder Next the arm links were inserted mated to be concentric with

the side holes of the covering cylinder, parallel to the slot face

in the driving pin’s triangular base. The front edges of both

arm links were mated to be parallel. All of these mates are

shown in Figure 105.

Figure 105: All of the mates

between the Arm Links and

the Covering Cylinder.

Arm Links, Driving Pin and the Claw Finger The Claw Finger’s retaining bolt holes were concentrically

mated to the driving pin holes and the arm link holes. Also

the front face of the Claw Finger was mated to the internal

face of the arm link. These mates are shown in Figure 106.

Figure 106: The mates

between the Arm Links, Claw

finger, the Driving Pin.

Insertion of Hex Bolts and Nuts Using the design library toolbox, standard hex bolts were

created and mated to the holes in the Arm Links, Driving Pin

and Claw Finger. Hex nuts were created in the same fashion

and mated to the ends of the hex bolts. These Bolts and nuts

were concentrically mated to their respective holes. This is

shown in Figure 107.


insertion of retaining bolts

and nuts and all relevant

mates.

31

Circular Pattern of Arm Links, Claw Finger, and Hex

bolts and nuts Circularly patterned the Arm Links, Claw Finger and retaining

nut and bolts as well as all relevant mates using the top edge

of the covering cylinder as the parameter. This is shown in

Figure 108.

Figure 108: The circular

pattern of the Nuts and Bolts,

Claw Finger, and Arm Links.

Claw Mounting platform and the Covering Cylinder Inserted the claw base platform into the assembly and mated

the top surface of the covering cylinder and the bottom surface

of the platform. And then attached the nuts utilizing the design

toolbox. This is shown in Figure 109.


mates between the mounting

platform and the covering

cylinder as well as the

retaining bolts.

32

Final Claw Subassembly

Shown in Figure 110.

Figure 110: The complete

Claw subassembly.

Base Sub-Assembly

In order to produce the final base assembly, the joint

assembly steps of the motor onto the main base needs

to be repeated for the other two rectangular prisms.

This base must be capable of withstanding the

conjoined weight of the triple arm system and the

claw assembly. The scaling factor of 20/3 for all the

components of the base was convenient for the

overall assembly because the scaled version of the

assembly held the same appearance as the smaller

version. Parametric equations and configurations

would have complicated the resizing process of the

base assembly even more.

Figure 111: Final Base Sub-Assembly

First, the front face of the motor fin was made

coincident to the back face of the rectangular prism.

This mate helps eliminate some of the translational

degrees of freedom of the motor.

Figure 112: Motor Coincident Face

33

The pattern of the hole in the motor was made

concentric to the hole pattern of the rectangular

prism. With this mate, the holes of the different parts

lined up perfectly with no surface interference. The

top motor face was made coincident to the bottom

cross-section of the rectangular piece. After a

combination of both of these mates, all of the

translations of the motor was erased

Figure 113: Motor Concentric Hole

The motor still has the ability to rotate at a fixed

point. To eliminate the rotation, a coincident mate

was applied on the top motor surface and the bottom

fin surface. Since this mate falls after the concentric

and coincident mates directly above, the motor is

complete fixed onto the rectangular prism of the main

base part (no degrees of freedom are present).

Figure 114: Motor Coincident Base

Next, the bolt was screwed onto the prism and the

motor. A concentric mate was applied on the inner

circular pattern of the prism and the outer circular

pattern of the bolt shaft.

Figure 115: Bolt Concentric Hole

In order to totally eliminate the translation of the

bolt, the bottom face of the bolt head was made

coincident to the surface of the rectangular prism

opposite to the surface where the motor and base

model mated. These bolt mates still provide a one

degree of freedom rotation of the bolt at a fixed

point.

Figure 116: Bolt Coincident Face

34

After the bolt, the washer was the next component

assembled. A concentric mate was issued in along

the circular patterns of the washer and the bolt. Since

the washer hole dimension was the same as the shaft

of the bolt, the washer was able to line up evenly

with the bolt.

Figure 117: Washer Concentric Hole

Another concentric mate was used in this assembly

between the washer face and the inner face of the

motor fin. The washer was the smallest component of

entire sub-assembly.

Figure 118: Washer Coincident Face

Lastly, the nut was included in the assembly right

after the washer. The same concentric was applied

between the circular pattern of the nut and the

circular pattern of the bolt.

Figure 119: Nut Concentric Hole

The nut bottom face was made coincident to the

washer face. After these two last mates were

applied, the assembly was secured.

Figure 120: Nut Coincident Face

35

Final Triple Delta Assembly

Top Delta to Final Base Assembly

To begin the final assembly, the Top Delta is

Connected to the Base Sub Assembly. First the Rod is

mated using a concentric and coincident mate.

Figure 121: The rod mates with

motor base sub assembly

The Rod is then mated concentrically with the Driving

Delta Arm of the Top Delta Sub Assembly. It is also

mated to the appropriate planes between the Rod and

the Driving Motor Arm.

Figure 122: The coincident mate

between planes of the rod and the

motor arm.

These steps are completed for the other two motors

and Driving Delta Arms. The Top Delta subassembly

and Base assembly are now complete.

Figure 123: The Top Delta

subassembly and Base assembly

36

Bottom Delta to Final Claw Assembly

To complete this, the Bottom Delta is mated to the

Final Claw Assembly by mating concentrically and

coincidently the Rod Joint ends to the connecting holes

in the Claw assembly base.

Figure 124: Ball Socket Joint mates

with Claw Mounting Platform

This is repeated for the other four Connections. The

Delta and Claw are now fully assembled.

Figure 125: Bottom Delta and Claw

fully defined in final assembly.

37

The Triple Delta Assembly is finally complete.

Figure 126: Final Triple Delta robotic

arm configuration.

38

Exploded View of Triple Delta Configuration

Figure 127. Showing the full assembly

exploded from the front view orientation

Figure 127.

Figure 128. Shows the Arm Base and top

delta exploded from front view orientation

Figure 128

39

Figure 129. Shows the Middle and Bottom

Delta exploded view from front view

orientation.

Figure 129

Figure 130. Shows the Claw exploded view

from front view orientation.

Figure 130

Mechanism Model Analysis

The robotic arm is constructed out of many unique selection of materials. The cost and

the machinability of each of the materials was not heavily considered in this robotic arm final

assembly because the fabrication budget was unknown. However, the materials were selected for

40

each part based on the weight and the longevity of the components when undergoing repetitive

motion and counteracting potential stresses and strains. The essential components of the claw

were made out of steel and titanium. The base platform itself was made out of steel and the

motors were coated with plastic. Most of the rods in the whole assembly were made out of either

steel or aluminum material. The platforms for the arms were made out of steel, and the ball joints

were fabricated out of polyester resin.

After the mass properties calculations were ran in SolidWorks, it was found that the

overall mass of the robotic arm was 648.15 lbs. This is heavy robotic arm given that the total

volume of the robotic arm is only 4878.8 in3. Components such as the main base platform, the

covering cylinder of the claw, and the arm and claw mounting platform contributed significantly

to this overall weight. The rods on the bottom-top delta were keep light in weight so that the

motor connecting arm will be capable of moving the assembly up and down. The center of mass

in the 3D graphics window came out to be (-5.73, -1.65, 6.63) inches. The density of the base

was tremendous at 0.29 lbs. /in3. The moment of inertias of the final assembly and the main sub-

assemblies all were significantly heavier along the Ixx, Iyy, and Izz directions.

The best solution to alleviate any issues that can occur in the long term with the robotic

arm is to either choose lighter materials to support the volume of the final product or simply

increase the overall size of the robotic arm. Also, understanding machining cost and the

availability of materials will also be crucial in designing the most realistic arm possible.

Table I: Mass Properties of Parts

Sub-Assembly Name Mass (lbs.) Density

(cubic in.)

Material

Base Hex Bolt 1 8.20E-01 2.90E-01 AISI 304

Hex Bolt 2 8.20E-01 2.90E-01 AISI 304

Hex Bolt 3 8.20E-01 2.90E-01 AISI 304

Motor Piece 1 2.76E+01 4.00E-02 Nylon 101



41

Washer 1 0.00E+00 4.00E-02 ABS

Washer 2 0.00E+00 4.00E-02 ABS

Washer 3 0.00E+00 4.00E-02 ABS

Nut 1 1.50E-01 1.00E-01 7075-T6 (SN)

Nut 2 1.50E-01 1.00E-01 7075-T6 (SN)

Nut 3 1.50E-01 1.00E-01 7075-T6 (SN)

Rod Piece 1 3.19E+00 2.80E-01 AISI 1045 Steel, CD



Motor Connecting Arm 1 7.65E+00 1.00E-01 3003-H12



Base Final Copy 1.47E+02 2.90E-01 AISI 316 Stainless Steel

Sheet (SS)

Claw Covering Cylinder 1 5.79E+01 2.80E-02 AISI 1020 Steel, Cold

Rolled

Arm Link 1 2.00E+00 2.80E-01 AISI 4320 Steel,

normalized

Arm Link 3 2.00E+00 2.80E-01 AISI 4320 Steel,

normalized

Driving Pin/Triangle base 9.97E+00 2.80E-01 Alloy Steel

Claw Finger 1 2.03E+00 2.90E-01 AISI 321 Annealed

Stainless Steel (SS)

Claw Mounting Platform 1 4.70E+01 1.70E-01 Titanium Ti-13V-11Cr-

3Al

42

Hex Bolt_Ai 25 2.50E-01 1.60E-01 Commercially Pure

Titanium (Ti-55)


Titanium (Ti-55)


Titanium (Ti-55)

Hex Nut_Ai 16 1.00E-02 1.00E-01 7075-T6 (SN)

Hex Nut_Ai 17 1.00E-02 1.00E-01 7075-T6 (SN)

Hex Nut_Ai 19 1.00E-02 1.00E-01 7075-T6 (SN)


Titanium (Ti-55)


Titanium (Ti-55)


Titanium (Ti-55)


Titanium (Ti-55)

Top Delta Ball_Joint 1 1.40E-01 4.00E-02 Polyester Resin

Ball_Joint 2 1.40E-01 4.00E-02 Polyester Resin








43









Ball_Socket 1 4.10E-01 2.60E-01 Ductile Iron
















44



Rod 1 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 2 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 3 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 17 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 18 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 22 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 31 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 32 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 33 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Middle Delta Arm_Platform 1 7.12E+01 2.80E-01 AISI 1020 Steel, Cold

Rolled

Bearing Mount Platform 1 8.80E-01 1.70E-01 Titanium Ti-8Mn,

Annealed

Bearing Mount Bolt 1 1.20E-01 1.00E-01 7075-T6 (SN)

Bearing1 <1> 4.00E-02 2.90E-01 AISI 304

Bearing1 <2> 4.00E-02 2.90E-01 AISI 304

Bearing1 <9> 4.00E-02 2.90E-01 AISI 304

Bearing1 <10> 4.00E-02 2.90E-01 AISI 304

Bearing1 <17> 4.00E-02 2.90E-01 AISI 304

Bearing1 <18> 4.00E-02 2.90E-01 AISI 304

Connected Arm 1 5.19E+00 1.00E-01 7075-T6 (SN)

New Connected Rod 1 4.90E-01 1.00E-01 3003-H14

45

























46

















Rod 7 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 8 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 9 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 25 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 26 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 27 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 28 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Rod 29 1.55E+00 1.00E-01 3003-H14, Rod (SS)

47

Rod 30 1.55E+00 1.00E-01 3003-H14, Rod (SS)

Bottom Delta Arm_Platform 1 7.12E+01 2.80E-01 AISI 1020 Steel, Cold

Rolled

Bearing Mount_Platform 1 8.80E-01 1.70E-01 Titanium Ti-8Mn,

Annealed

Bearing Mount Bolt 1 1.20E-01 1.00E-01 7075-T6 (SN)

Bottom Connecting Arm 1 4.82E+00 1.00E-01 7075-T6 (SN)

New Connecting Rod 2 4.90E-01 1.00E-01 3003-H14

Bearing1 <3> 4.00E-02 2.90E-01 AISI 304

Bearing1 <4> 4.00E-02 2.90E-01 AISI 304

Bearing1 <11> 4.00E-02 2.90E-01 AISI 304

Bearing1 <12> 4.00E-02 2.90E-01 AISI 304

Bearing1 <15> 4.00E-02 2.90E-01 AISI 304

Bearing1 <16> 4.00E-02 2.90E-01 AISI 304





Rod 35 1.55E+00 1.00E-01 3003-H14

Rod 36 1.55E+00 1.00E-01 3003-H14

Rod 37 1.55E+00 1.00E-01 3003-H14

Rod 38 1.55E+00 1.00E-01 3003-H14

Rod 39 1.55E+00 1.00E-01 3003-H14

Rod 40 1.55E+00 1.00E-01 3003-H14

48

Ball Socket 70 4.10E-01 2.60E-01 Ductile Iron
























49

Table II: Final Assembly and Subassemblies’ Mass Properties

Mass Properties of the Final Assembly

Configuration: Default

Coordinate system: -- default --

Mass = 648.15 pounds

Volume = 4878.80 cubic inches

Surface area = 10917.85 square inches

Center of mass: ( inches )

X = -5.73

Y = -1.65

Z = 6.63

Principal axes of inertia and principal

moments of inertia: ( pounds * square

inches )

Taken at the center of mass.

Ix = (-0.01, 1.00, -

0.00)

Px = 72014.42

Iy = (-0.99, -0.01,

0.13)

Py = 750120.92

Iz = (0.13, 0.00, 0.99) Pz = 750195.78

Moments of inertia: ( pounds * square

inches )

Taken at the center of mass and aligned

with the output coordinate system.

Lxx = 750098.28 Lxy = -4020.39 Lxz = 0.86

Lyx = -4020.39 Lyy = Lyz = -

50

72042.68 1730.95

Lzx = 0.86 Lzy = -1730.95 Lzz =

750190.16


inches )

Taken at the output coordinate system.

Ixx = 780354.90 Ixy = 2110.80 Ixz = -

24638.42

Iyx = 2110.80 Iyy =

121842.30

Iyz = -8820.93

Izx = -24638.42 Izy = -8820.93 Izz =

773261.68

Mass Properties of the Completed Claw

Subassembly

Configuration: Default-_flexible1


The center of mass and the moments of inertia are output in the coordinate system of

The Final Assembly





X = -5.48

Y = -51.13

Z = 6.75



51

inches )


Ix = (-0.00, 1.00, -

0.00)

Px = 3090.37

Iy = (-0.71, 0.00,

0.71)

Py = 4116.26

Iz = (0.71, 0.00, 0.71) Pz = 4116.26


inches )



Lxx = 4116.26 Lxy = -0.01 Lxz = -0.00

Lyx = -0.01 Lyy = 3090.37 Lyz = -2.21

Lzx = -0.00 Lzy = -2.21 Lzz = 4116.25


inches )


Ixx = 366714.61 Ixy = 38215.89 Ixz = -5047.73

Iyx = 38215.89 Iyy = 13405.92 Iyz = -

47074.58

Izx = -5047.73 Izy = -

47074.58

Izz =

364595.09

Mass properties of Base Motor Arm

Sub Assembly

Configuration: Default-_flexible1



52

Actually the final assembly materials





X = -5.95

Y = 27.31

Z = 6.53



inches )


Ix = (-0.67, 0.00,

0.74)

Px = 15679.85

Iy = (0.74, 0.00,

0.67)

Py = 15687.00

Iz = (-0.00, 1.00, -

0.00)

Pz = 27494.01


inches )



Lxx = 15683.80 Lxy = 14.12 Lxz = -3.59

Lyx = 14.12 Lyy =

27493.94

Lyz = 27.00

Lzx = -3.59 Lzy = 27.00 Lzz =

15683.13

53


inches )


Ixx = 108863.77 Ixy = -

19201.15

Ixz = -4599.94

Iyx = -19201.15 Iyy = 36726.21 Iyz =

21109.64

Izx = -4599.94 Izy = 21109.64 Izz =

108009.30

Mass properties of Base final copy

Configuration: Default



Actually the final assembly materials

Density = 0.29 pounds per cubic inch





X = -5.93

Y = 36.29

Z = 6.56



inches )


Ix = (1.00, -0.01, Px = 6769.30

54

0.07)

Iy = (0.07, 0.01, -

1.00)

Py = 6844.77

Iz = (0.01, 1.00, 0.01) Pz = 11227.76


inches )



Lxx = 6769.94 Lxy = -32.76 Lxz = 5.07

Lyx = -32.76 Lyy =

11226.81

Lyz = -55.72

Lzx = 5.07 Lzy = -55.72 Lzz = 6845.08


inches )


Ixx = 200166.27 Ixy = -

30646.26

Ixz = -5527.82

Iyx = -30646.26 Iyy = 22348.44 Iyz =

33791.88

Izx = -5527.82 Izy = 33791.88 Izz =

199128.2

Mechanism Kinematics

In order to show the movement capability of this design, a motion analysis and study was

performed. Rotational motors were added to the rotating rods in the arm base within the fully

modeled assembly. These simulate the mechanisms utilized in actual delta robotic arms. Also in

order to perform this analysis the triple delta configuration was simplified to a double delta

configuration, this significantly reduced the number mates in the assembly and made the model

much less computationally intensive. This simplification allowed analysis to be calculated

despite Central Processing Unit and Graphics Processing Unit limitations and accelerated the

study. The motor type utilized was the segment motor. This allows for control over the both the

55

distance (in degrees) the motors rotate as well as the duration of said rotation. This was

determined to be the most efficient motor type in terms of the configuration time.

The first step in demonstrating this designs ability to move in three dimensional space,

was to have the model collapse and extend along the central axis. This is done through synced

rotation of all three of the base motors. Rotating outward from the center of the base causes the

connecting arms to tilt down which extends the model. This extending motion was a set as

positive motion in the study. Rotation inward towards the center of the model causes the

connecting arms to rotate upwards collapsing the model along the central axis. This movement is

performed in the motion study from 0 seconds to 3.75 seconds

The next step in the motion analysis is to show translational motion along the plane for

which the central axis is normal. This type of motion is accomplished by inducing negative

rotation on one motor and positive rotation on the remaining two motors. This action moves the

arm along the bottom plane from the central axis toward the negatively rotating motor and away

from the positive direction of rotation. This movement is performed in the motion study from

3.75 seconds to 15.5 seconds

The final step to demonstrating the movement of the assembly was to simulate the arm’s

ability to first extend down, then actuate the claw and then finally retract up its vertical axis. This

was done to imitate the actual movement of the arm if it was being utilized to elevate an object

from a lower position to a higher position. This movement is performed in the motion study from

15.5 seconds to 21.6 seconds.

The acceleration, velocity and displacement was calculated for a point at the center of the

vertical face of the claw finger. This point was chosen due to the fact that it best tracks the

largest magnitudes of acceleration, velocity and displacement experienced by any part in the

final assembly. The following plots denoted the magnitude of these vectors in the Y direction as

the model underwent its 3-dimensional movement capability motion study.

As shown in the plots, the point undergoes dramatic changes in displacement (Plot 1),

velocity (Plot 2) and acceleration (Plot 3) as the beginning and at the end of the motion. This is

due to the fact that the study was done with respect to the y direction and at the beginning of the

study the arms capability to collapse and extend is demonstrated which will result in high

displacement, acceleration and velocity peaks in the y direction. The middle of the study

(between 4.8 seconds and 16.8 seconds) was during the demonstration of the arms ability to

move in a planar fashion and therefore the acceleration, displacement and velocity vectors

remain constant. The acceleration and velocity centers around 0 during this period of the study

which stands to reason. The final part from 16.8 seconds to 24 seconds shows the simulation of

the extending of the arm, opening and closing of the claw fingers, and the subsequent retraction

56

of the arm to finish the motion. This was done to calculate the motion of the delta arm during a

typical use cycle.

Plot 1: Linear

Displacement (y-

direction)

Plot 2: Velocity

(y-direction)

Plot 3:

Acceleration (y-

direction)

Conclusion

After modeling the parts, creating the assembly, and performing the motion study, there

are important aspects to be made. Even though the parts are very basic to model, assembling and

making the motion study were not simple to construct since assembling took many step to make

it and managing over 300 mates, and the motion study was very demanding and went through

many trial and error processes to acquire good animation. This was due to the complexity of the

57

mechanism of the multi delta configuration by which there were many ball and socket joints to

be calculated into the motion study and the fact that each ball joint had 3 degrees of rotational

freedom. The driving mechanism would only be constrained by the limiting angle set on the ball

to socket joint and the rotational extent of the motor.

58

References

[1] Dassault Systèmes - SolidWorks Corporation, 2011 “Student’s Guide to Learning

SolidWorks® Software.” PMS0119-ENG

[2] Simon, S. 2014, “Page 1,” Multi-delta robotic arm design creates large-build 3D prints in

small spaces http://www.3ders.org/articles/20141226-multi-delta-roboticarm-design-creates-

large-build-3d-prints-in- small-spaces.html (accessed Feb 24, 2015).

http://www.3ders.org/articles/20141226-multi-delta-robotic-

multi-delta robotic arm modeling project report

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