A Novel Approach to the Part Orientation Problem for Robotic Asse

To limit the scope of the design problem, this researchwill focus on end-effector designs that can be used in conjunction with a SCARASelective Compliant Assembly Robot Arm type robot..

Master's Theses (2009 -) Dissertations, Theses, and Professional Projects

A Novel Approach to the Part Orientation Problem for Robotic Assembly Applications

Brian James Slaboch

byBrian J Slaboch, B.S.

A Thesis Submitted to the Faculty of the Graduate School,

Marquette University,

in Partial Fulfillment of the Requirements for

the Degree of Master of Science

Milwaukee, WisconsinMay 2011

ROBOTIC ASSEMBLY APPLICATIONS

Brian J Slaboch, B.S

Marquette University, 2011

SCARA (Selective Compliant Assembly Robot Arm) type robots are themost common type of assembly robots These robots have four degrees of freedom(three rotational and one translational) Typically these robots are used for

assembly tasks that take place along a vertical axis Many times, however, assemblytasks take place along a non-vertical axis

To account for non-vertical axis assembly, parts must be fed in a properorientation to allow for correct assembly Parts feeders and specialized end-effectorsare typically used to feed parts in their proper orientation This thesis investigates anovel end-effector that can be used to feed parts for industrial assembly

applications Specifically, the purpose of the novel end-effector is to provide a

SCARA robot with an added selectable degree of freedom

This end-effector aims to bridge the gap between complex anthropomorphicgrippers and simple binary grippers The approach is novel in that the end-effectorinteracts with the environment to produce the added degree of freedom New pathplanning algorithms were developed to work in conjunction with the novel

end-effector A prototype end-effector was designed, built, and tested to prove thevalidity of this new approach

Brian J Slaboch, B.S

I would first and foremost like to thank Dr Philip A Voglewede for providing mewith this great opportunity This work could not have been completed without hissupport and guidance In addition, I would like to thank Dr Mark Nagurka and Dr.Joseph Schimmels for their insightful comments and suggestions A special thanksgoes to Jinming Sun and Bryan Bergelin for their continued support and helpfuladvice I would also like to thank Tom Silman and Ray Hamilton for their work inthe machine shop Finally, the I would like to thank my family and friends for theirencouragement and guidance

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

DEDICATION ii

TABLE OF CONTENTS iii

LIST OF TABLES v

LIST OF FIGURES vi

CHAPTER 1 Introduction 1

1.1 Parts Feeding Systems 4

1.2 End-Effector Design 5

1.3 Summary 8

CHAPTER 2 Mechanical Design 10

2.1 Design Requirements 10

2.2 Engineering Requirements 11

2.3 Quality Function Deployment 13

2.4 Conceptual Design 13

2.4.1 Magnet Device 13

2.4.2 Ratchet Device 14

2.4.3 Mechanical Brake 14

2.4.4 Friction Device 14

2.5 Concept Selection 15

2.6 Configuration Design 17

2.7 Parametric Design 19

CHAPTER 3 Path Planning 22

3.1 Path Planning 22

3.1.1 Horizontal Line Path 23

3.1.2 45◦ Angle Path 24

3.1.3 Shortest Distance Path 25

3.2 Path Planning Algorithms 26

3.2.1 Horizontal Line Path Algorithm 27

3.2.2 45◦ Path Algorithm 29

3.2.3 Shortest Distance Path Algorithm 32

3.2.4 Return Path 34

CHAPTER 4 Dynamic Analysis 37

4.1 Lagrange’s Equations of Motion 37

4.2 Newton-Euler Equations of Motion 42

4.2.1 Vertical Motion 42

4.2.2 Rotation about the θ3 Axis 43

4.2.3 Rotation about the θ1 Axis 45

TABLE OF CONTENTS — Continued

CHAPTER 5 End-Effector Manufacturing and Testing 50

5.1 Material Selection 50

5.2 Positioning Hinge Selection 51

5.3 Detail Design 53

5.4 Prototype Testing 54

5.4.1 Rapid Prototype Test 1 56

5.4.2 Rapid Prototype Test 2 57

5.4.3 Design Modifications 58

5.5 Final Design 58

5.5.1 Final Design Test 1 59

5.5.2 Final Design Test 2 59

5.5.3 Discussion 60

CHAPTER 6 Contribution and Future Work 62

6.1 Contributions of this Research 62

6.2 Future Work 63

6.2.1 Dynamic Analysis 63

6.2.2 Kinematic Analysis 64

6.2.3 Stress Analysis 65

6.2.4 Robustness 65

REFERENCES 66

APPENDIX A 68

LIST OF TABLES

2.1 Pairwise Comparison 11

2.2 Engineering Requirements 12

2.3 Weighted Rating Method 16

2.4 Scale 16

4.1 Maximum Accelerations and Velocities 48

5.1 Costs 53

LIST OF FIGURES

1.1 Manipulation Flow Chart 2

1.2 SCARA ROBOT 3

1.3 Lever Assembly onto Vertical Post [1] 3

1.4 Angled Peg Assembly using Adept Viper Robot 4

1.5 Utah/Mit Hand [2] 5

1.6 Pivot Grasp [3] 6

1.7 Schunk SKE Pneumatic Swivel Head 7

1.8 Metamorphic Gripper 8

1.9 Underactuated Robot 8

2.1 Magnet Concept 14

2.2 Concept Sketch: Friction Device 17

2.3 Configuration 1 18

2.4 Configuration 2 18

2.5 Configuration 3 19

2.6 Critical Dimension 20

3.1 Pivoting Gripper Device Schematic 23

3.2 Horizontal Line Path 24

3.3 Angle Path 25

3.4 90◦ Pick and Place [4] 25

3.5 Shortest Distance Path 26

3.6 Simplified Geometry 27

3.7 Horizontal Line Path Schematic 28

3.8 θf vs h (L = 8.9 cm) 29

3.9 θf vs h 30

3.10 45◦ Angle Schematic 30

3.11 d vs θf 31

3.12 αmin 33

3.13 Shortest Distance Path Schematic 33

3.14 Return Path Schematic 34

3.15 Return Path 35

4.1 SCARA Robot with End-Effector 38

4.2 Reference Configuration 40

4.3 Free Body Diagram, Vertical Motion Case 41

4.4 Free Body Diagram, Rotation about the θ3 Axis 44

4.5 τ vs θ4 for θ3 rotation 44

4.6 Free Body Diagram, Rotation about the θ1 Axis 45

4.7 τ vs θ4 for θ1 rotation (θ3 = 90◦) 47

4.8 τ vs θ4 for θ1 rotation (θ3 = 0◦) 47

4.9 τ vs θ4 for Horizontal Motion 48

5.1 Reell PHK Positioning Hinge 52

LIST OF FIGURES — Continued

5.2 Detailed Drawing of the Pivot Arm 54

5.3 Detailed Drawing of the Base 55

5.4 CAD Model 55

5.5 Rapid Prototype 56

5.6 Test 1 with Rapid Prototype 57

5.7 Test 2 with Rapid Prototype 58

5.8 Final Design 59

5.9 Final Design with Gripper 60

5.10 Final Design Test 1 60

5.11 Final Design Test 2 61

A.1 45◦ Angle Schematic 68

A.2 Relation Between ǫ and l 69

CHAPTER 1Introduction

Assembly lines were first made famous by Ford Motor Company at the start

of the twentieth century Mass production of automobiles revolutionized

manufacturing processes Businesses realized that a low unit cost per manufacturedpart led to a competitive advantage Companies continue to find innovative

manufacturing processes that allow them to lower costs and increase quality

The assembly lines created by Ford have changed significantly from the early1900’s In many cases, robotic manipulators have replaced human workers on

assembly lines In the automobile industry robots are used for spot welding andother assembly tasks Robotic manipulators can be used to decrease assembly timeand reduce human error However, one drawback of robotic manipulators is thatthey lack flexibility Parts must be fed in a specific part orientation prior to

assembly Current parts feeding devices can lead to high capital costs and offer littleflexibility There is a need to create more efficient and flexible ways to feed

anthropomorphic hands provide the desired flexibility for industrial assembly tasksbut are difficult to control due to the coordination of all of the degrees of freedom(DOF) of the system Conversely, binary grippers are easy to control but do notprovide the necessary flexibility

This research aims to bridge the gap between the two and determine a way

to combine the flexibility gained from using anthropomorphic hands with the

simplicity of binary grippers To limit the scope of the design problem, this researchwill focus on end-effector designs that can be used in conjunction with a SCARA(Selective Compliant Assembly Robot Arm) type robot This research aims tocreate an end-effector that provides an added DOF to a SCARA robot withoutadding significant complexity SCARA type robots were chosen because these arethe most commonly used industrial assembly robots [5]

Part Orientation

Parts Feeding Systems

End-Effector Designs

Anthropomorphic Hands

Stanford/JPL Hand [10]

Utah/Mit Hand [3]

? Binary Grippers

Electrical or Pneumatic Parallel Jaw Gripper

categorized into parts feeding systems and end-effector designs

Four DOF SCARA type robots (three rotational and one translational,Fig 1.2) are used in many industrial robotic assembly applications The SCARArobot shown in Fig 1.2 allows for translational motion as well as a rotation aboutthe z-axis.1 SCARA type robots work well for assembly tasks and pick and placeoperations that take place along a vertical axis (i.e., the direction of the

gravitational force) This is the most common type of assembly operation Pick andplace assembly tasks are preferred because the parts feeding operation is greatlysimplified

An example of vertical axis assembly is shown in Fig 1.3 The lever shown inFig 1.3a must be picked up, rotated, and then assembled onto the vertical post in1

Specifically, this type of motion is known as Sch¨ oenflies motion.

Fig 1.3b In its natural resting position (Fig 1.3a), the lever cannot be assembledonto the vertical post using only the DOF of the SCARA robot The part must berotated prior to assembly on the vertical post.

z

x o

There are also many robotic assembly tasks and pick and place operations inwhich a part must be assembled on an axis other than the vertical axis For

instance, consider the six-axis Adept robot shown in Fig 1.42 The six-axis Adeptrobot is able to pick a part oriented along the vertical axis, and it is able to place it

on an angled board This type of angled assembly operation is not possible usingonly the four DOF of a SCARA robot The part must be rotated prior to placing it

on the angled board

The previous two examples show that proper part orientation is critical forindustrial assembly tasks This chapter reviews previously developed solutions to2

Figure 1.4 is used with permission from Adept Technologies Inc.

Figure 1.4: Angled Peg Assembly using Adept Viper Robot

the part orientation problem

The most common approach to the part orientation problem is to use a partsfeeding system Parts feeding systems are typically costly for flexible assemblybecause they are usually designed for one specific part, and therefore any partchange adds significant cost There are applications in which parts feeders areadvantageous For instance, parts feeders work well for small parts such as screwsthat have to be stood upright prior to assembly However, in many situations

capital costs can be reduced significantly if vibratory bowl feeders can be

eliminated According to Boothroyd [6], parts feeders are responsible for 30% of thecost and 50% of the failures in assembly operations

Peshkin and Sanderson [7] developed a parts feeding system that uses aconveyor belt with rigid fences to orient parts prior to assembly They developed acomplete algorithm that can be used to orient polyhedral parts prior to assembly.One drawback from this solution is that the algorithm only works for polyhedralparts Additionally, the algorithm may not be able to find a solution

A similar approach to that of Peshkin and Sanderson was completed byZhang et al [8] in which parts are fed on a conveyor belt and toppled over by pins.This type of sensorless orientation has the same drawbacks as those of Peshkin and

Sanderson Another conveyor belt design was completed by Causey and Quinn [9].Causey and Quinn created a conveyor belt design in which three conveyors worktogether This system works for a variety of parts, but it still requires three externalconveyors and a separate control algorithm for each part that is fed.

The main drawback with any parts feeding system is that it typically lacksflexibility The capital costs are typically high, and the parts feeding system must

be adjusted for each part In an attempt to simplify this process, many researchershave focused on parts feeding by grasping and manipulation

Developing end-effectors that feed parts by grasping and manipulation allowsfor a more flexible system Many early end-effector designs mimic the human hand.Examples of these are the Stanford/JPL hand [10], the Utah/MIT Hand [2]

(Fig 1.5), and the Barrett Hand [11] While these end-effectors are extremelyflexible, they are difficult to use in an industrial setting due to the required

computational power and coordination of the DOF

There have also been attempts at creating industrially feasible end-effectors

to orient parts Goldberg et al produced a pivoting gripper [3] that uses ball

bearings to rotate a part under the force of gravity They subsequently proved thatthe pivoting gripper could be used to orient a part arbitrarily in six DOF using a

four DOF SCARA type robot [4] This gripper uses a series of pivot grasps asshown in Fig 1.6 In this design, a part is grasped between two ball bearings androtated under the force of gravity By completing a series of these pivot grasps thepart can be manipulated The major drawback with this system is that picking up apart repeatedly takes too much time when compared to picking up a part andassembling it directly.

Ziesmer and Voglewede improved upon this design by creating a

metamorphic [12] gripper that uses metamorphic joints that change between fixedjoints and spherical joints [13] This reduces the amount of time to manipulate thepart This design is limited in that the part to be picked up must have symmetricalcontact points Ziesmer and Voglewede’s design is unique in that they used anexternal fixed post to pivot the part to a desired angle One drawback from thisdesign is that it does not work for delicate parts that cannot be pressed into anexternal fixed finger Additionally, the ability to use this gripper depends heavily onthe part geometry

In 2002 Zhang et al showed that it is possible to orient parts while graspingthem [8] Their device is shown in Fig 1.3 The gripper contact points are used tomanipulate the part prior to vertical axis assembly Once again, this approach onlyworks for polyhedral parts Furthermore, the approach lacks flexibility because thepin design must be generated for each part to be manipulated

A more industrial approach to solving this problem is to attach an electricalrotary actuator to the end of a SCARA type robot to provide an added DOF.However, electrical rotary actuators require a separate drive controller from that ofthe robot Motors may lead to significant downtime and added cost Another option

is to attach a pneumatic rotary actuator to the end of a SCARA type robot toprovide an added DOF An example of a pneumatic rotary actuator is the SchunkSKE pneumatic swivel head shown in Fig 1.73 The Schunk SKE is a low weightthree position pneumatic actuator geared clean environments such as assembly andpackaging Pneumatic rotary actuators offer less flexibility than electrical actuators

as they can generally only travel to two or three positions

Researchers have also focused on underactuated systems that take advantage

of the dynamics of the system to manipulate a part Lynch and Mason [14] created

a one DOF robot that manipulates a part by flipping it in the air and exploiting thedynamic effects This work is intriguing, but it is not industrially feasible because itrequires complex dynamic modeling as well as a complex control system

Additionally, it lacks robustness

Lynch et al also created a 3-DOF robot that exploits dynamic properties tocontrol a passive joint [15] Fig 1.9 shows the 3-DOF system The first two joints3

Figure 1.7 is used with permission from Schunk.

Figure 1.8: Metamorphic Gripper [13]

are active and the third joint is a passive joint As shown this robot is in the

horizontal plane By moving the actuated joints appropriately the third passivejoint will move to the desired position One problem with this system is that not alltrajectories are achievable at higher speeds In addition, the dynamics change if therobot is oriented in the vertical plane or if there are changes with friction

As was shown in this chapter there are two common approaches to theproblem of orienting parts for an assembly task These two approaches can becategorized into parts feeding systems and end-effector designs End-effectors canfurther be categorized as complex anthropomorphic hands or simple binary

grippers Complex anthropomorphic hands are not industrially feasible due to thecoordination of all of the DOF, and simple grippers do not offer enough flexibilityfor an industrial assembly task This research aims to simplify the part orientationproblem by creating an industrially feasible end-effector that is both flexible andsimple The goal is to create an end-effector that provides an added DOF to aSCARA robot without adding significant complexity.

Chapter 2 will provide details of the mechanical design process This will befollowed by a kinematic analysis in Chapter 3 Next, a dynamic analysis of thissystem will be provided in Chapter 4 Following this analysis, Chapter 5 will focus

on the end-effector manufacturing and testing Finally, Chapter 6 will explore ideasfor future work

CHAPTER 2

Mechanical Design

This chapter outlines the design process as well as the decision making thatoccurred during the design process This chapter begins with a section outlining thedesign requirements Engineering requirements were then determined based on thedesign requirements After determining the engineering requirements, a standardquality functional deployment process was used to determine the relationship

between the engineering requirements and the design requirements The next step

in the design process was to complete the conceptual design Once the final conceptwas chosen, different design configurations were created The final step in the designprocess was to determine specific part dimensions

In this design five design requirements for the end-effector were chosen Theend-effector should be:

1 Robust: high number of cycles

2 Economical: low capital cost

3 Fast: short cycle time

4 Repeatable: low positioning error

5 Flexible: easily adaptable for different parts

To determine the relative weight of each design requirement a pairwisecomparison was completed (Table 2.1) Each design requirement was compared toeach of the other design requirements When comparing two design requirementsthey are denoted with either a one or a zero A one indicates a design requirement

of greater importance This leads to a rough estimate of how important each designrequirement is relative to the others For instance, in Table 2.1 robust is compared

to economical in the first column It was thought that it was more important for thesystem to be economical than robust Thus, a one was given for economical and azero for robust Robust was then compared against each of the other design

requirements The column labeled “Total” shows the total number of ones that eachdesign requirement received This can then be expressed as a percentage showingthe relative importance of each of the design requirements Table 2.1 shows thatrobustness is the most important design requirement and accuracy is the leastimportant However, the system should still be low cost, fast, and flexible Thistable is inherently subjective, but it is useful because it shows that none of thedesign requirements can be ignored Additionally, the table of importance weights isalso used to evaluate different conceptual designs This analysis will be completed

in Section 2.4

requirements must be met to satisfy the design constraints This is not meant to be

an exhaustive list, but it will at least be used to help guide the design process

Table 2.2: Engineering RequirementsSubfunction Engineering Characteristic Units Limits Robust number of cycles - > 43200 Economical number of custom parts - < 3

cycle time s < 2 time to troubleshoot min < 5 Flexibility range of motion rad - π

2 to π 2 Repeatability positioning error mm ± 2.5 Simplicity number of actuators - 0Each of the design requirements and the corresponding limits was chosen for

a particular reason The reasons for each choice are listed below:

• 43,200 cycles was chosen so that the robot could operate at 30 cycles perminute for 24 hours

• The number of custom parts was chosen to be less than three to keep capitalcosts down Specifically, this will keep machining costs low

• A low weight of 4.45 N was chosen because it allows for heavier parts andgrippers to be manipulated

• A fast cycle time was critical in keeping costs down, and therefore a

reasonable cycle time of 2 seconds was chosen This is consistent with therobustness requirement

• It should take less than five minutes to troubleshoot any problems that mayoccur during operation This will lower costs by reducing the amount ofdowntime

• The range of motion was limited to π rad Typically, this is an acceptablerange of motion for an assembly task

• The device must be repeatable to within ±2.5 mm

• The number of actuators was chosen to be zero This is important because itallows the end-effector to be controlled using the robot controller

2.3 Quality Function Deployment

After the design requirements and engineering requirements are established it

is possible to determine the relationship between them using a House of Quality.This information can be used to determine the relative weight of each of the

engineering requirements The results show that a lower overall weight is critical for

a successful design There are multiple reasons for this A lighter end-effector

corresponds to shorter cycle times, increased robustness, and lower cost

Additionally, a lighter end-effector allows a larger (in mass) part or gripper thatmay be attached to the end of a robot

In this section the relationship between the design requirements and theengineering requirements was determined using a House of Quality The next

section will focus on the conceptual design phase In this section different designconcepts will be evaluated and one will be chosen to be developed further

Conceptual design is perhaps the most important part of the design process

A design may be either doomed for failure or primed for success early on in thedesign process Conceptual design is useful for analyzing alternative designs based

on guiding physical principles To aid this process a weighted rating method wasused to evaluate different conceptual designs

The first design was based on the idea of locking and unlocking the

rotational joint using a combination of magnets as well as inertial forces Figure 2.1shows a concept sketch of this device A fixed stop is placed at an angle θ withrespect to the vertical As the robot accelerates the gripper would rotate until thetwo magnets touched This would lock the gripper at a desired angle After theassembly task is completed the robot would accelerate in the opposite direction, andthe inertial forces would unlock the joint

Magnet

Fixed

X Y

Another idea was to use a mechanical brake similar to a mechanical brake on

a bicycle It was thought that a similar idea could be used to stop the rotation of apivoting gripper The mechanical brake would be actuated using an additionalpneumatic actuator

Lastly, a device was considered in which controlled friction could be used toachieve the desired rotation The controlled friction concept brought together thebenefits from the other three concepts The design is based on using positioninghinges (also called constant torque hinges) that provide a constant torque resistancethroughout its range of motion These types of hinges are identical to those

generally used in laptops Thus, when a user moves the screen of a laptop from one

angle to another the screen becomes fixed at that angle.

The idea is to apply the same concept to rotate a robotic gripper Figure 2.2shows the conceptual sketch for the controlled friction concept As shown in thefigure, a positioning hinge is attached to the end of the SCARA robot The

positioning hinge is attached to a pivot arm, and the pivot arm is attached to thegripper If an external force presses against the pivot arm then the gripper willrotate To provide an external force a fixed post is used As the end of the robotmoves from position 1 (Fig 2.2a) to position 2 (Fig 2.2b) the end of the robotmoves along the −x-axis, and the pivot arm presses against the fixed post causingthe gripper to rotate This will provide the system with an added DOF Thus, afour DOF SCARA type robot would have a selectable fifth DOF

Four different concepts were considered, but only one of these concepts could

be developed further To help determine which concept to develop further a

weighted rating method was used Table 2.3 shows how the weighted rating methodwas used to evaluate different conceptual designs The four concept alternativeswere rated on a scale from 0 − 4 (Table 2.4) for each of the criteria The rating isthen multiplied by the importance weight to determine the weighted rating Thesum of the weighted ratings for each concept provides an overall rating for thatconcept The results from Table 2.3 show that controlled friction idea achieved thehighest score

This type of analysis is inherently subjective Therefore the designer shouldconsider which concept alternative should be developed further Three of the

concepts had a “showstopper” that eliminated it from contention For instance, themagnet idea was not chosen because it did not provide enough flexibility While aratchet-like device could be used to move the gripper to different angles while

continually locking an unlocking, this device is difficult to manufacture and not veryrobust The brake required the use of an additional actuator which adds significantoverall complexity to the system (The friction device did not have an obvious

showstopper, and therefore this was the device chosen for further development.)

Criteria Importance Weight Magnetism Ratchet Mechanical Brake Friction

Rating WR Rating WR Rating WR Rating WR

Very Good 4

There are numerous other advantages to using this design It was reasonedthat the overall design would be lightweight due to the fact that there are few parts.This is important because a low weight will allow for heavier parts and end-effectors

to be used In addition, robust positioning hinges are readily available for purchase.This will allow for a low-cost device with a high degree of robustness and accuracy.Furthermore, it was thought that with proper path planning techniques the devicewould be repeatable to within the specified limits1 Lastly, the system is “flexible”

in that any type of gripper may be attached to the pivot arm This is an importantconcept for this design Many times specialized grippers are designed to pick up aparticular part However, these specialized grippers are not designed to manipulatethe part in any way An advantage of the controlled friction concept is that

specialized grippers may be still be utilized

In this section four different conceptual designs were evaluated The

controlled friction concept was chosen to be developed based on the results of theweighted rating method as well as the fact that three of the designs had an obvious1

This will be explained in greater detail in Chapter 3.

Positioning Hinge

Gripper

Part Fixed Post

Figure 2.3 shows the first configuration considered In this configuration apivot arm is attached to a positioning hinge The positioning hinge is attached to ahousing which is attached to the end of the robot The gripper is attached to thepivot arm While in theory this configuration could work, there were numerousissues with the configuration The first is that the center of mass of the gripper isfar away from the positioning hinge Thus, an extremely strong positioning hingewould be required to to hold the gripper in place Additionally, this configurationdoes not work well from a path planning perspective This will be explained ingreater detail in Chapter 3

Figure 2.4 shows the second configuration considered This configuration

Pivot Arm

Housing

Gripper Robot Attachment Point

Another advantage of this configuration is that it works well from a path planningperspective This will be explained in greater detail in Chapter 3

The second configuration can be improved upon as shown in Fig 2.5

(Configuration 3) In both configurations the housing and the pivot arm are the two

manufactured parts First consider the housing In configuration two, the

positioning hinge slot is not centered with respect to the housing, but in

configuration three it is centered with respect to the housing Symmetry is

important because it simplifies the design The reason that the slot in configurationtwo is not symmetric to the housing is that it is desired that when the pivot arm is

in the vertical position it aligns with the center axis of the robot attachment Thiswill simplify the path planning Next consider the pivot arm In configuration twothe pivot arm is not centered over the positioning hinge This is changed in

configuration three by creating a housing around the positioning hinge This creates

a simplified design

Configuration three was the final configuration chosen The next step in thedesign process is to determine the exact dimensions of the end-effector Some of thedimensions are chosen arbitrarily while other critical dimensions are chosen based

on detailed analysis The next section will outline which dimensions were criticaldimensions and which dimensions were chosen arbitrarily

techniques Many of the dimensions on the two manufactured parts are not designvariables For instance, fillets were included in the design to reduce stress

concentrations The fillets were selected to be standard sizes (i.e., 0.3175 1

8
or0.635 1

4
mm (in.)) These are not critical for the design The critical dimension inthis design is the distance L from the center of the positioning hinge to the end ofthe pivot arm as shown in Fig 2.6

L

This dimension is critical because the success or failure of the design is based

on choosing this dimension correctly There are many design tradeoffs that need to

be considered There are multiple reasons why a designer would want the pivot arm

to be as long as possible A longer pivot arm:

1 reduces the external force required to rotate the gripper while still allowing for

a strong positioning hinge Thus, heavier grippers and parts can be

accommodated which makes the system more flexible

2 increases the positioning accuracy, as will be shown in Chapter 3

3 allows for a greater range of motion in certain path planning techniques

On the other hand, it is advantageous to have a shorter pivot arm A shorter pivotarm:

1 reduces weight Less material is needed both for the pivot arm as well as thehousing.

2 increases rotation speed

3 increases the available workspace of the robot

As can be seen from the previous two lists, the length of the pivot arm iscritical Chapter 3 will be used to determine the appropriate length of the pivotarm with respect to different path planning techniques Once the length of the pivotarm is chosen from a path planning perspective, a dynamic analysis will be

completed in Chapter 4

CHAPTER 3

Path Planning

There are many different aspects to motion planning for a robotic system Acommon misconception is that motion planning involves only collision detection.However, in robotic assembly applications, motion planning may include the process

of grasping the part, transferring the part, and positioning the part on a

subassembly Thus, both physical and geometrical constraints could be taken intoaccount [17]

One subset of motion planning is path planning Path planning considers thebasic motion planning problem from a geometrical point of view This means thatthe physical interaction between components is ignored (i.e., it is purely a kinematicproblem) Thus, the friction forces between the pivot arm and the fixed post as well

as the impact between the pivot arm and fixed post will be ignored

This chapter outlines different path planning algorithms that can be used toachieve the desired gripper rotation These algorithms are unique in that it ispossible to use the built in controls from the robot to control the angle of rotation

of the gripper There is no need for any external control software This is a distinctadvantage over using an electrical rotary actuator

There are many different ways to move the robot’s end-effector in the

xy-plane to achieve a desired angle of rotation However, depending on the

application there are certain paths that are more suitable than others The

following sections outline different path planning algorithms that can be used fordifferent assembly applications In each of the different paths the center of thepositioning hinge, point A, will be the point of interest This is because this point isfixed relative to the end of the robot In the following figures, a dotted line with anarrow will denote that the positioning hinge moves along that line

Fixed Post

Positioning Hinge Pivot Arm

Gripper

h t

One way to achieve the desired rotation is to move the end-effector in astraight horizontal line path along the x-axis as shown in Fig 3.2 As the

end-effector moves along the x-axis the pivot arm makes contact with the fixed postand the force from the fixed post causes the positioning hinge to rotate The desiredangle of rotation is denoted as θf

The main advantage to this path is that the gripper is rotated during normaloperation of the robot There is little wasted motion Additionally, this path

planning motion is time independent There is, however, one distinct disadvantage

to this type of path planning; the gripper cannot be rotated a full 90◦ from thevertical position There is a limit on the possible angle of rotation due to the

diameter of the fixed post as well as geometrical constraints from the mechanicaldesign This will be explained further in the following sections

The advantage to this path is that the gripper can be quickly pivoted from

0◦ to 90◦ This angle is necessary for a wide variety of applications For instance,consider the pick and place operation shown in Fig 3.4 (Adapted from Goldberg et

al [4]) With a conventional SCARA robot the rectangular parts would need to befed in their final upright configuration At high feeding speeds this may cause theparts to topple over However, with the ability to rotate the parts 90◦ from a

horizontal to a vertical position the parts can be fed laying flat or vertically Thiswould allow for higher feeding speeds

X Y

The next section will outline another type of path in which the goal was todetermine the shortest possible distance the robot’s end-effector would need totravel to achieve the desired angle of rotation

The shortest distance path that is useful for certain assembly tasks This isnot necessarily the “best” path that works for every assembly operation This path

is called the shortest distance path because the goal was to determine the shortestpossible distance the robot’s end-effector would need to travel to achieve the desired

angle of rotation, θf.

X Y

Line of Rotation

Consider the solid line that is at an angle of θf in Fig 3.5 This line is fixed

in space, and it will be denoted as the line of rotation This line is offset andtangent to the fixed post If the positioning hinge is moved from its initial position

to any position on the line of rotation the gripper will be rotated by an angle θf.For example, the positioning hinge could move along a 45◦ line until it reaches theline of rotation This is exactly what was proposed in the previous subsection

The quickest way to achieve a rotation of θf is to move the positioning hingefrom its initial position in a straight line perpendicular to the line of rotation Thistype of motion, however, does have limits For instance, it is impossible to rotatethe gripper 90◦ using this type of motion 90◦ rotation would correspond to movingthe positioning hinge along the y-axis Doing so would not provide any rotation

Three different paths have been introduced in this section The next sectionwill provide the path planning algorithms that can be implemented in order toutilize the three different paths

This section presents the path planning algorithms for the different paths.For each of the path planning algorithms it is assumed the pivot arm begin in

contact with the fixed post at θ = 0 (Fig 3.6) Further, it is assumed that themlocation of the fixed post is known relative to the base frame of the robot Thus,point A(xi, yi) in Fig 3.6 is the starting position of the center of the positioninghinge, and it is known relative to the fixed post and thus the base frame of therobot The goal is to determine the final position B(xf, yf) that the positioninghinge must be moved to in order to achieve the desired rotation θf.

The fixed post has a radius, r, and the pivot arm has a thickness t Thepivot arm length, h, is defined as the length from the center of the positioning hinge

to the center of the fixed post In this particular case, the rectangular shape of thepivot arm makes the geometry more difficult than is necessary To simplify thegeometry, the fixed post of radius r can be viewed as a circle of radius R where

R = r +2t The pivot arm can then replaced by a line as shown in Figure 3.6

X Y

The horizontal line path algorithm is simple, but has limits on the possibleangle of rotation The reason for this is that there are geometrical constraints due

to the mechanical design In this type of motion the positioning hinge begins at aknown point A and moves to point B along the x-axis The kinematic equationsgoverning this type of motion are

to the end-effector moving past the fixed post then the end-effector would need to

be moved around or under the fixed post to continue motion along the x-axis Theexcess motion of moving around or under the post would lead to higher cycle times

The angle of rotation is dependent on both L and h Thus,

Equation 3.4 shows that there are limitations on θf due to the constraints placed on

h and L In the chosen design L = 8.9 cm, r = 0.41 cm, and R = 0.88 cm Due tothe physical constraint of the housing that surrounds the positioning hinge, h must

be at least 3.3 cm In addition, for the max case it is desirable that the top of the

pivot arm aligns with the top of the fixed post The reason for this is that it ensuresthat the pivot arm makes solid contact with the fixed post Thus, h has a maximumvalue of L − R

2 = 8.46 cm

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Figure 3.8 shows how θf changes as a function of h with L = 8.9 cm It can

be seen from the plot that 0.54 rad (31◦) < θf <1.29 rad (74◦) for horizontal linepath motion Figure 3.9 shows a plot of θf vs h as L is varied from 5.1 cm to 24 cm

in 1.27 cm increments The line furthest to the left corresponds to L = 5.1 cm, andthe farthest to the right is L = 25.4 cm The dotted line is L = 8.9 cm From

Fig 3.9 it is clear that the design follows the law of diminishing returns That is, as

L keeps increasing there is not a large increase in the range for θf In fact, L wouldneed to be increased to 25.4 cm to increase the range of θf by 20◦ This is notrealistic as L would be too long to be practical Thus, a path planning algorithm isneeded that allows for a full 90◦ rotation This leads to the 45◦ path algorithm