Group AChristopher Back

Joseph Ashwin FranklinKwong voon Wong

Chen Lin

Machines and Mechanisms II MAE 512 Final Project

SHRIMP Robot Front Leg Design

• Introduction

• Design Constraints and Requirements

• Synthesis Description

• Synthesis Design Process

• Synthesis Results

• Prototype Development

• Analysis Description

• Analysis Design Process

• Analysis Results

• Overall Performance of Mechanism Designs

Overview

Introduction

• The Goal of this project is to design and optimize the four-bar system used in the front leg of the SHRIMP legged-wheel robot in order to allow the robot to climb over the obstacles of heights (H=2R, H=4R, H=2R)

• We are also required to come up with a four bar system that reduced the peak torque required and reduced the fluctuations of the torque through one cycle.

Design Constraints And Requirements• Device must be a Four-bar linkage that either be a Crank-

Rocker or Double Crank

• Must agree with Grashof Criteria to be able to predict behavior

• Must pass through all necessary points to climb an obstacles

• The Device must be compact (Sum of 4 links must be small)

• Should have base points located within the body of robot.

• The linkage system should have reduced peak torque and torque fluctuations to avoid active control of motor

3 Position Motion Generation by Analytical Synthesis

Synthesis Matrix Form(3 point)

M+W +Z =P1;M+W*exp(b2) +Z*exp(a2) =P2;M+W*exp(b2+b3)+Z*exp(a2+a3) =P3; N+ U +S =P1; N+U*exp(g2) +S*exp(a2) =P2; N+U*exp(g2+g3)+S*exp(a2+a3) =P3;

Mechanism Synthesis Procedure:

• Pose problem as 3 point precision problem

• Make use of 3 point synthesis equations

• Free choices are (db2,db3,dg2,dg3,da2 da3)

• Assign arbitrary values for (db3,dg3,da2 and da3)

• Vary angles (db2 and dg2) to determine a possible range for feasible mechanisms.

• We also needed to see if these feasible mechanisms have base pivots M and N within the chassis of the robot.

• We made use of a series of surface plots to perform our search.

Figure 1: Surface Plot of DB2,DG2 and usability criterion

Figure 2: Surface plot of a narrow band for search of DB2, DG2, and usability criterion

Figure 3: Surface plot of DG2,DB2 and sum of the link lengths

Figure 4: Surface plots of base pivots M and N against usability criterion

Results from Initial Synthesis Analysis:

• We see that the values for M and N indicate that there are no feasible mechanisms that have a base pivot within the chassis of the robot

• The surface plot analysis still gave us some ideas regarding the angle ranges for possible designs.

Mechanism Synthesis cont…

• We now posed problem as a two point synthesis problem using the appropriate synthesis equations .

• Now we have free choices as (db2,dg2 and da2)

• Varying these parameters we performed a search for the base pivots (M and N) locations within chassis.

• To do this we again made use of surface plots

Figure 5: Real and Imaginary parts of M and N

Figure 6: Shows the region of M (0.3 < Rm<1) and the Im(.75<1m<1.25) are all feasible

Mechanism Synthesis Continued:• From previous set of surface plots we obtained a feasible region for M and

N location.

• Now we manually tune the angles to obtain a desired output path.

• We know that using the synthesis equations does not guarantee the

mechanism will pass through the desired points in the same configuration.

• To check if mechanism passes through the required points we make use of

a series of animations.

Path trace of mechanism for H=2R case

Path trace of mechanism for H=4R case

Path trace for mechanism for H=6R case

Matlab Animation

Prototype Development

Height of Stairs = 2R

Prototype Development

Height of Stairs = 4R

Prototype Development

Height of Stairs = 6R

Prototype Development

Static Balancing

• Position Analysis

• Loop Closure Equations

• Velocity Analysis

• Differentiation of Loop Closure Equations

• Force Analysis

• Newton Euler Method

• Torque Variations for a Crank Rocker

• Lowest Peak Torque

• Least Torque Fluctuation

• Balancing to reduce Torque Fluctuation

Analysis

Purpose was to identify which parameter effects Torque variation to improve design

Variation db2 Max Torque110 40.8347

113.6667 17.37117.3334 9.722121.0001 8.623124.6668 7.712128.3335 6.8453

132.00 6.7466

Variation dg2 Max Torque85 7.62

87.5 7.125890 6.7466

92.5 6.41295 6.1358

Variation da2 Max Torque7 9.72178 8.41959 7.47

10 6.7466

Sensitivity Analysis

Peak Torque Variations Lowest Torque

Behavior of Mechanism DesignsCase H=2R

0 50 100 150 200 250 300 350 400-2

-1.5

-1

-0.5

0

0.5

1

1.5

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Peak Torque plot of Feasible Designs

0 50 100 150 200 250 300 350 400-1.5

-1

-0.5

0

0.5

1

1.5

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

Peak Torque Variations Lowest Torque

Behavior of Mechanism DesignsCase H=4R

0 50 100 150 200 250 300 350 400-4

-3

-2

-1

0

1

2

3

4

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Peak Torque plot of Feasible Designs

0 50 100 150 200 250 300 350 400-3

-2

-1

0

1

2

3

4

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

Peak Torque Variations Lowest Torque

Behavior of Mechanism DesignsCase H=6R

50 100 150 200 250 300 350

-10

0

10

20

30

40

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

0 50 100 150 200 250 300 350 400-6

-5

-4

-3

-2

-1

0

1

2

3

4

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

• Lowest Peak Torque coincides with least Fluctuation

• Static Balancing - to reduce Fluctuation and decrease fatigue and strain on the Mechanism

• Moved CG to point of rotation• Reduced fluctuation but

increase in peak Torque

Behavior of Mechanism DesignsFluctuation Reduction

Lowest Peak Torque

Behavior of Mechanism DesignsCase H=6R

Least Fluctuation after balancing

0 50 100 150 200 250 300 350 400-6

-5

-4

-3

-2

-1

0

1

2

3

4

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Peak Torque plot of Feasible Designs

0 50 100 150 200 250 300 350 400-4

-3

-2

-1

0

1

2

3

4

5

6

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Peak Torque plot of Feasible Designs

Lowest Peak Torque

Behavior of Mechanism DesignsCase H=4R

Least Fluctuation after balancing

0 50 100 150 200 250 300 350 400-2

-1

0

1

2

3

4

5

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Balanced Fluctuation of Feasible Designs

0 50 100 150 200 250 300 350 400-3

-2

-1

0

1

2

3

4

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

Lowest Peak Torque

Behavior of Mechanism DesignsCase H=2R

Least Fluctuation after balancing

0 50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1

1.5

2

Driving Angle (deg)

Tor

que

(New

ton

Met

res)

Lowest Torque Fluctuation of Feasible Designs

0 50 100 150 200 250 300 350 400-1.5

-1

-0.5

0

0.5

1

1.5

Driving Angle (deg)

Torq

ue (N

ewto

n M

etre

s)

Peak Torque plot of Feasible Designs

• Our Design trace a path that will allowed the Front Leg to Climb the stair

• Although the Front leg will climb higher than it need, it can be an advantage when we have higher flight

• The performance of our design can better be better determined with a real prototype

• The Fourbar criteria limits our imagination to come out with better design

Overall Performance of SHRIMP Robot Front Leg Design

Questions?