MAE 512 Final Project Presentation Design for the front linkage of a shrimp wheeled robot Rob Desjardins Mark Szymanski Christopher Wirz.

MAE 512MAE 512Final Project PresentationFinal Project Presentation

Design for the front linkage of a Design for the front linkage of a “shrimp” wheeled robot“shrimp” wheeled robot

Rob Desjardins

Mark Szymanski

Christopher Wirz

AbstractAbstract In this project, the parameters of a four-bar linkage In this project, the parameters of a four-bar linkage

on the front of a Shrimp platform will be optimized on the front of a Shrimp platform will be optimized to climb over obstacles of given height 2H, 4H, and to climb over obstacles of given height 2H, 4H, and 6H.6H.

Candidate parameters were generated using the Candidate parameters were generated using the synthesis and analysis equations presented in synthesis and analysis equations presented in lecture, minimizing peak torque and torque lecture, minimizing peak torque and torque fluctuations.fluctuations.

These parameters were then tested using SolidEdge These parameters were then tested using SolidEdge / Dynamic designer and MATLAB for further / Dynamic designer and MATLAB for further evolution of the design. evolution of the design.

Design Procedure (flow chart)Design Procedure (flow chart)

Our task was to design a mechanism Our task was to design a mechanism capable of moving from point A to point capable of moving from point A to point B in the diagram below.B in the diagram below.

Procedure:Procedure:

We first drew a simple diagram to We first drew a simple diagram to represent the front end of the shrimp.represent the front end of the shrimp.

Synthesis equations were developedSynthesis equations were developed This gave us a good initial guess for R valuesThis gave us a good initial guess for R values

The goal is to minimize the value of (r1+r2+r3+r4+r5+r6) by varying the following parameters:

1 2 3 4 6 2,1 2,2 3,1 3,2 4,1 4,2 6,1 6,2 1 1 2s s s s s s s s x dx dx

61 4

4 4,1 6 6,11

4 4,2 6 6,21

6 32

6 6,1 2 2,1 3 3,1

6 6,2 2 2,2 3 3,2

ii i 1

i s i si1 1 1

i s i s 4i1 2

6i ii1

2i s i s i s

1 13

i s i s i s

x 0e e eHr x dxe e e2r

x dx He e er

x 0e e e rH

e e e x dxr2

e e e

1 2

1

i

x dx H

Also, loop closure equations were Also, loop closure equations were analyzed and differentiated for our case.analyzed and differentiated for our case.

This allowed us to obtain equations for This allowed us to obtain equations for the velocities and accelerations of the the velocities and accelerations of the various points and links.various points and links.

Force AnalysisForce Analysis The forces on the The forces on the

aforementioned 4-bar were also aforementioned 4-bar were also analyzed.analyzed.

The diagrams below show the The diagrams below show the conventions used for the conventions used for the analysis.analysis.

Sum of the forces in the X

Sum of the forces in the Y

Sum of the moments about the center of mass

12,x 14,x 1 1F F m x

12,y 14,y 1 1 1F F m g m y

1 112,x 1 14,x 1

1 1 11 1

12,y 1 14,y 1

r rF sin F sin

2 2 Ir r

F cos F cos2 2

Additional RelationsAdditional Relations6 6

5 5

12,x 21,x

12,y 21,y

F F

F F

14,x 41,x

14,y 41,y

F F

F F

32,x 23,x 53,x

32,y 23,y 53,y

F F F

F F F

34,x 43,x 63,x

34,y 43,y 63,y

F F F

F F F

56,x 65,x

56,y 65,y

F F

F F

4 1

5,6 6,5

Force Equation MatrixForce Equation Matrix

18 equations, 18 unknowns…18 equations, 18 unknowns…

1 1 1 11 1 1 1

2 2 2 22 2 2 2

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

r r r rs c s c 0 0 0 0 0 0 0 0 0 0 1 0 0 0

2 2 2 21 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

r r r rs c 0 0 s c 0 0 0 0 0 0 0 0 0 0 0 0

2 2 2 20 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0

0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0

3 3 3 3 3 3 3 33 3 3 3 3 3 3 3

4 4 4 44 4 4 4

5 55 5

r r r r r r r r0 0 0 0 s c s c s c s c 0 0 0 0 0 0

2 2 2 2 2 2 2 20 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0

r r r r0 0 s c 0 0 0 0 s c 0 0 0 0 1 0 0 0

2 2 2 20 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0

r r0 0 0 0 0 0 s c 0

2 2

21,x

21,y

41,x

41,y

23,x

23,y

5

5 55 5

6 6 6 66 6 6 6

F

F

F

F

F

F

F

r r0 0 0 s c 0 1 0 1

2 20 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0

r r r r0 0 0 0 0 0 0 0 0 0 s c s c 0 0 1 1

2 2 2 2

1 1

1 1

1 1

2 2

2 2

2 2

3,x 3 3

53,y 3 3

43,x 3 3

43,y 4 4

63,x 4 4

63,y 4 4

65,x 5

65,y

1

5

6

65

m x

m g y

I

m x

m g y

I

m x

F m g y

F I

F m x

F m g y

F I

F m

F

5

5 5

5 5

6 6

6 6

6 6

x

m g y

I

m x

m g y

I

Finding MassFinding Mass For T6061 Aluminum, the density of the For T6061 Aluminum, the density of the

material is 2.7g/ccmaterial is 2.7g/cc The cross section area is 1cm^2The cross section area is 1cm^2

where is in cm.where is in cm.2

n n 3

gm r 2.7 1cm

cm

nr

Finding Moment of InertiaFinding Moment of Inertia2

n nzc,n

m rI

12

Initial trial:Initial trial:

To begin, a simple 2-point synthesis was To begin, a simple 2-point synthesis was performed with the points A and B as performed with the points A and B as given by the project description.given by the project description.

The values for the position of the ground The values for the position of the ground points and the change in angle of r4, r1, points and the change in angle of r4, r1, and r5 were defined before the analysis and r5 were defined before the analysis was performed.was performed.

Initial 2 point Synthesis ApproachInitial 2 point Synthesis Approach

Next iterationNext iteration From this point, a GUI was created in From this point, a GUI was created in

MATLAB to display the path of any MATLAB to display the path of any given 4-bar mechanism.given 4-bar mechanism.

The GUI allowed any parameter to be The GUI allowed any parameter to be varied and output an animation of the 4-varied and output an animation of the 4-bar requested and the force and torque bar requested and the force and torque graphs with respect to x-position.graphs with respect to x-position.

GUIGUI

Ex: Varying the path by varying R4Ex: Varying the path by varying R4

Our “Best” Link LengthsOur “Best” Link Lengths

r1 = 30 cm r2 = 60 cm r3 = 20 cm r4 = 65 cm r5 = 55 cm r6 = 33 cm

SolidEdgeSolidEdge

This final configuration was modeled in This final configuration was modeled in SolidEdge for visual purposes.SolidEdge for visual purposes.

ENDEND

Questions?