Kinematic Analysis and Prototype

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

Our main goals for this linkage is to provide a smooth oscillating motion. Although our prototype was designed with no specific angle in mind, we do intend to modify and experiment with our prototype to achieve an oscillation centered with the pivot link (lower left joint) and about 10 

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

The initial approach for the kinematic analysis was to analyze the linkage using Stephenson's six bar linkage analysis approach by creating two vector loops and using the common linkage between the two to find the missing values. Unfortunately, this method was extremely complicated and we were unable make significant progress within a long period of time and eventually moved on to simply using the displacement, velocity, and acceleration plots in motiongen. Below is a link to a google colab that was used initially to analyze the first vector loop - designated as the 4 bar loop consisting of the crank - to find the properties of the oscillating bar.

https://colab.research.google.com/drive/1coDzB8L6NwIw3rEnqCVQiPSXJW28SUmu?usp=sharing

Similar to the oscillating linkage, we did not focus on force analysis since we are primarily interested in the position profile of the end of the linkage. The goal of this linkage is to have a more vertical motion profile with still some lateral movement to account for the change in angle while moving the whole body forward.

The videos below show the animations for both the original Klann linkage (approximately the one used for the prototype) and our modified version with a more vertical profile.

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.

Next Steps

Our next steps are going to be to start finalizing our plans for the connection between the two linkage systems. We currently intend to use a bevel gear to simultaneously drive the oscillating and Klann linkages at a 1:1 gear ratio. With that figured out we will refine our link measurements to achieve the most optimal position profiles and then plan out the orientation and mounting of the linkage systems on a base. This base needs to look like the silhouette of a spider's body so we have to work around this shape. Once the mounting of the linkage systems, motor, and power source are determined and properly integrated into the intended spider shape we can start fabricating the links and assembling them, being sure to test them and ensure they run smoothly and with no collisions or jams. At this point the hardest part is over and we can start the full assembly of our project, designing and producing an aesthetically pleasing 3D body for the spider. We intend to do this my using spaced out layers of laser cut wood slotted perpendicular to the base to form the framework of a 3D body around all our components.

Bill of Materials