3.2 Walker Project Prototype

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:

Position Analysis

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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.

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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

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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.

Iteration Documentation

We did our preliminary iteration using a python script that calculates and plots the motion profile with the linkages visible. This script also includes sliders to adjust all necessary values. Initially, the motion profile was much more circular and not flat at the bottom, which would have led to unstable walking motion.

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After tweaking the values, we ended up with a shape that is much more efficient as there is a flat section on the bottom of the motion profile that exists for a significant duration of the input crank’s rotation.

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After this, we doubled the link lengths to result in the animation and the velocity and acceleration plots above. We used those measurements directly in CAD to mock up our first physical iteration. This consisted of slot shapes that all have center to center distances set equal to the correct link lengths.

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However, the bearings we are using for our prototype are very unstable, and the inner race is able to twist, so our first physical iteration had much more lateral movement than we desired. On our next iteration, we doubled up the bearings in order to geometrically constrain their rotation to purely radial. Additionally, because the first iteration was only slot shapes, the actual end point of point P (according to the motion plot) was not on a vertex of the triangular shape, so we modified that link to perfectly match the profile from the python script. Additionally, the base was modified so that there is a stand whose bottom aligns with the flat portion of the motion profile. This allows for easier visualization of the motion and allows us to see how smoothly it can actually walk. A rubber band was then placed along the outside of the ground contact linkage to increase friction, leading to our final prototype:

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Our final iteration will use laser-cut acrylic instead of 3D printed PETG for our linkages as it will increase stiffness which is necessary to reduce buckling risks. Additionally, we will use bushings instead of the small, low tolerance bearings we used in the prototype.

Bill of Materials