Kinematic Analysis and Design

Oscillating Linkage Kinematic Analysis:

Mobility Calculation:

L = 4, J = 4, 1/2J = 0

DOF = 3L - 3 - 2J - 1/2J

= 3(4) - 3 - 2(4)

= 1 DOF

Grashof Calculation:

L = 67, S = 9, P = 55, Q = 40

L + S < P + Q

67 + 9 < 55 + 40

Therefore linkage is Grashof

Ground - Adjacent Crank-Rocker

Klann Linkage Kinematic Analysis:

Mobility Calculation:

L = 6, J = 7

DOF = 3L - 3 - 2J - 1/2J

= 3 * (6 - 1) - 2 * 7

= 1 DOF

Grashof Calculation:

S = 15, L = 32, P = 22, Q = 32

L + S < P + Q

32 + 15 < 22 + 32

Therefore linkage is Grashof

For the analysis for this linkage, the six bar Klann linkage was first simplified into a root four bar linkage.

Design Process:

The process for designing and producing our prototype focused on refining the proportional lengths of the two most important linkage systems. For our leg linkage, based on the known Klann Linkage, we aimed to minimize lateral movement but not completely get rid of it. The small amount of lateral movement is meant to compensate for the slight lateral movement caused by the arc of the oscillating linkage. With these two movements opposing and timed oppositely we want to create as close to a straight line path of motion as possible. 

First step was to prepare our linkage designs for production. We decided on using the laser cutter and plywood to produce all our links as it would be the easier, quickest, and most effective method. Our prototype links were purposely left without bearing slots and produced at a smaller scale than we expect our final product to be in order to minimize material usage and time. Rather than connect every link via bearing and dowel we simply drilled small holes in our linkage pivot points and created pin joints using a bit of steel wire. We were able to create working linkages for both systems. And experiment with different length links to alter the path our systems

Timeline:

Design and Production Preparation - Nov 3-5

Production & Assembly - Nov 6

Troubleshooting - Nov 7

Reflection:

In the making of the prototype we were able to produce working linkage systems with minimal complications. However, for the Klann linkage we realized our original design would end up resulting in two links colliding mid motion, not allowing for a complete rotation. We solved this issue by shortening the length of our driven link. Additionally, we discover that increasing the length of one of our ternary links reduces the lateral movement of the end link, creating a more desired position profile.

For the oscillating linkage, the main issue we ran into was the orientation of our links in the system to minimize space as we would need to fit 8 of these systems on our body. Additionally, we realized that the link that would have the Klann Linkage mounted on it needed to be the highest linkage in the system to avoid interference during motion.

Lastly, we realized that this project would require large amounts of ball bearings and dowels and using them is likely to increase the size of our project. Thus, we are considering using a different method of joining our links, likely some form of pin or nut and bolt.

Bill of Materials