13.4 Kinematic Analysis

Mechanism Description

The robot uses an inverted slider-crank mechanism, where contraction of the elastic elements drives the slider outward, producing vertical leg extension and lift-off.

Link lengths used in the analysis:

• l1=4l_1 = 4l1​=4

• l2=5.0l_2 = 5.0l2​=5.0

• l3=3.5l_3 = 3.5l3​=3.5

Mechanical Advantage Analysis

A mechanical advantage (MA) analysis was performed to understand force transmission throughout the motion. Results show that the mechanism exhibits lower mechanical advantage in the highly compressed configuration, with output force increasing as the mechanism extends. As the linkage approaches its straighter configuration, the mechanical advantage improves, producing larger output forces near full extension.

This behavior is ideal for jumping, as it concentrates force output near takeoff while allowing energy to be stored over a longer actuator stroke.

Key Insight

The inverted slider-crank trades speed for force near its singular configuration, making it well-suited for impulsive energy release but highly sensitive to alignment, friction, and manufacturing imperfections.

Motor Torque Calculations (For DC Motor) - The purpose of this was to select the required motor driver, motor and battery for our jumping robot

Summary of Tables

To make sure that we choose the correct DC motor to tighten the pulley (have adequate torque and speed), we calculated the optimal motor speed characteristics, from weight and friction assumptions of the jumping robot, and jumping height and time to tighten requirements. The motor never stalled (even with 15 rubber bands). The failures of this mechanism came from the geometric design under high loading conditions.

Table A: Geometric Factors (Note that the highlighted components are the factors that we are trying to optimize through selection of electronic components

Table B: Torque Speed Curve Calculations

Table C: Kinematic analysis using Calculated Values