1. Overview

Our main goal for our project is for our robot to jump ideally two feet. Though we have decided on the geometry we are going to use, the final robot will probably use different linkage lengths in order to maximize jumping force; we nondimensionalized our lengths for this purpose. In our analysis we have theta1 as our input to obtain position for our joints, which gets us velocity, acceleration, and ultimately force. This is a different inversion than our final configuration, which would involve our input manipulating theta4 instead; we will continue analysis using the latter inversion for link length optimization. The goal for the analysis is to set up a framework to find force values in order to know what stiffness we need for the springs that will be used on our robot to achieve our desired jump.

2. Mobility Calculation

The calculation above applies to our current linkage configuration used for analysis. Our final linkage system includes another link to ground (a rail system), which further constrains our system to 1DOF.

3. Linkage Labels

4. Velocity Analysis

We conducted basic velocity analysis using a set of 4 position equations with 4 unknowns to solve the system. In the system, we use theta1 as our input and took the derivative of these equations to obtain velocity values.

5. Acceleration Analysis

We conducted acceleration analysis using the velocity values above. We took the derivative of velocity in order to obtain acceleration values for these plots.

6. Force Analysis

We conducted basic force analysis using the calculated acceleration values above. Linkage lengths were scaled in inches and converted into metric units, and masses were calculated off the resulting volumes based off the density of 1/4" acrylic available in TIW; this yielded estimated force values in Newtons. Due to the difference in inversion in this analysis, point F (what would typically be input) has a significantly greater force output than point G, showcasing that the mechanical advantage desired from this linkage configuration does exist. Future steps involve doing this calculation with theta4 as input to get a better scale on mechanical advantage and using the resulting values to optimize for different link length combinations.

7. Linkage Angles and Animation

With theta1 as the input, we obtained other linkage angles for the system which are labeled by color.

Future steps involve doing this calculation with theta4 as input to get a better scale on mechanical advantage and using the resulting values to optimize for different link length combinations. This will also be followed by FEA analysis in order to get more concrete force values for our final designed linkages.