Mechanism Kinematic Analysis

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 that moves about 10 degrees from this center axis to either side. This, when having the Klann linkage mounted on it with a distance of about 8 cm from the pivot axis to the tip of the "leg", should produce a leg reach of around 3 cm. 

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.