1. Kinematic Analysis

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.

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.

Linkage Labels

1.1 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.

1.2 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.

1.3 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.

1.4 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.

2. Physical Prototype

2.1 Iteration 1: Drawings

We began by drawing the individual linkages and labeling each link and important angles. In the Project Proposal we proposed a 7-link mechanism. During the kinematic analysis step of this phase, we found 7 links were causing the velocity equations to diverge, so we reduced the number of links from 7 to 6.

2.2 Iteration 2: Cardboard

We used the drawings and initial kinematic analysis to quickly cut our links out via cardboard. We secured the links together with screws and nuts. We left out the CAM device at this stage to showcase the mechanism design. Our cardboard prototype showed a range of motion that matched closely with the results of the kinematic analysis, which enabled us to proceed to a higher fidelity prototype.

2.3 Iteration 3: CAD

We created a 3D design based on the knowledge gained from drawings and cardboard prototype iterations. The mechanism’s range of motion proved to be acceptable relative to the link lengths. In this phase, we discovered that the length of the CAM needed to be precisely controlled to maximize the motion of link 1, the “foot link” while preventing its collision with other links. After this testing, we chose to leave the CAM out of this prototype build. We will include it in the final build when we include the motor.

2.4 Final Iteration: Laser Cut Acrylic

We cut the 6 links out of acrylic based on the CAD design and assembled them using nuts and bolts as joints. We attached a torsional spring across links 3 & 4 using zip ties. The resulting motion was mostly satisfactory and closely matched previous analyses. 

2.5 Lessons Learned

1. We need a spring with a higher K-constant to generate sufficient force to lift the body off of the ground.
2. The spring mounting system must be robust to ensure minimal movement of the spring related to links 3 & 4.
3. The CAM shape and size must be delicately designed in such a way that it fully extends the spring while also quickly getting out of the way of the spring action.
4. A foot is required between the end of link 1 and the ground to provide stability and potential an additional compression spring.
5. We need to replace the nuts & bolts with rods & bearings to reduce friction and prevent loosening at the joints.

3. Bill of Materials