Mathematical modeling with polynomial functions of a cam profile through kinematic analysis of the follower

In the present research, the profile of a cam for a cam-follower-piston-heel system was designed, simulating the vertical forces exerted by a person's foot while walking on the heel. This system has the potential to contribute to technological innovation in quality testing for footwear companies in the region. Force vs. time data were obtained during a stable walking cycle, establishing the relationship between displacement and the simulated force. The mathematical modeling of the profile employs polynomial functions, defining 9 boundary conditions, resulting in an 8th-degree polynomial. The cam, designed based on its solution, complies with the fundamental law of cams (smooth curves for velocity and acceleration). To ensure that the pressure angle between the cam and the follower is less than 30°, an eccentricity of 0, a primary radius of 3 inches, and a base radius of 2 inches were determined. This ensures efficient force transmission in the follower's direction of motion. The cam-follower system was modeled in SolidEdge.