3.3 Kinematic Analysis

3.3 Kinematic Analysis

The goal of this analysis is to relate the actuator input to the resulting leg trajectory, and to evaluate whether the mechanism produces a smooth and repeatable walking motion. Position, velocity, and acceleration behavior were examined to assess gait smoothness, motion transmission, and the suitability of the linkage for locomotion.

The current prototype is based on a symmetric slider-linkage mechanism with a single input and one degree of freedom, allowing the system to be driven by one continuous actuation input.

Main Parameters:

  • L1 (ground) = 106.2 mm

  • L2 (crank) = 41.8 mm

  • L3 (rocker) = 98.4 mm

  • L4 (purple) = 67.3 mm

  • Total base footprint = 154.5 mm at maximum extension

Mobility Calculations:

Grubler Equation: M = 3(4-1) - 2(4) - 0 = 1 DOF

Position Analysis

This simulation was mainly used to iterate on the walker design by adjusting link lengths and offsets to see how the foot path changed.

By tuning parameters, we're able to shape the trajectory to get a flatter ground contact and enough clearance during the step. It helped us quickly test different configurations and converge on a motion that looks stable and practical before building the physical prototype.

Velocity Analysis

The velocity analysis comes directly from differentiating the four-bar vector loop.

From the velocity plot, the mechanism produces a naturally non-uniform gait: the foot slows down near the transition points and moves faster through the middle of the cycle. This slower motion near contact helps make foot placement smoother.

Acceleration Analysis

Force Analysis

During the rotation, the minimum mechanical advantage, calculated by w2/w4 is 1.184. However, the minimum mechanical advantage is applicable during ground contact, so within a threshold of point P being 5 mm from the ground, to account for any wobble, the minimum mechanical advantage is 1.639. Once the final walker has been desgined, the mechanical advatnage can be used with the forces due to the robot’s weight and friction with the ground, along with a safety factor to account for internal bending, to calculate the required motor output torque.