Kinematic Analysis - JG
Mobility
It is important that this mechanism has only one degree of freedom, that way the input rotation serves as the one and only driving factor for the entire mechanism. Below is Gruebler's Equation for Degrees of Freedom for this mechanism:
M = 3L - 2(J1) - (J2) - 3
M = 3(4) - 2(4) - (0) - 3 = 1 DOF
Kinematic Analysis
The main point of a mechanism such as this is to experience a quick return motion when your input reaches a certain point in its rotation. The graphs below demonstrate the ideal output velocity:
The important takeaway from both of these graphs is the large spike in both angular and linear velocities at approximately 0.5 seconds in this model. This large spike indicates that we will have the exact quick return action we are hoping for. Below is the animation from PKMS used to derive these velocities.
We can also see that we will experience a Coriolis acceleration at the joint connecting links 2 and 3. This acceleration is caused by the joint experiencing sliding as well as rotation simultaneously. The acceleration is noted on the animation above.
We can also manually solve for values at points of interest at one moment in time. Below is a link to the manual calculations for position, velocities, and acceleration.
Some of the most important considerations for this analysis relied of the length of link 2 and the distance between O2 and O3. To achieve a stable quick return, as well as maximizing the ratio between the quick and slow return, I experimented with several combinations of length. I eventually decided on a 1:2 length ratio, where link 2 was half of the length of the ground between joints. This allowed for a smooth full rotation of my input link, with a reasonable increase in velocity during the quick return. While a length ratio of close to 1:1 may produce a maximum velocity increase, we would have to sacrifice the controllability of the final mechanism. We would also be risking creating a high-stress point that may lead to failure with the materials used.