Energy Consumption Analysis of a Rolling Mechanism Based on a Five-Bow-Shaped-Bar Linkage

To reveal the relationship between the center of mass (CoM) trajectory of a closed five-bow-shaped-bar linkage and its energy consumption, this paper presents a trajectory planning method based on the workspace of the CoM. Using different height points located on the symmetric centerline of the workspace of the CoM as via points, the CoM trajectory is planned by combining cubic polynomials with Bézier curves based on quadratic Bernstein polynomials. Herein, the system energy consumption is obtained by integrating the product of generalized velocity and generalized force versus time, where the generalized force is calculated by Lagrange’s equation including the Rayleigh dissipation function. Then, two schemes of dynamic rolling are proposed to compare, and the theoretical results show that the system consumes less energy under the sinusoid scheme when the via point height is lower and the via point of higher height is more suitable under the modified trapezoidal curve scheme. Furthermore, this paper combines the locomotion simulation software to design the locomotion of the mechanism’s CoM trajectory under two schemes in detail and verifies the correctness of the theoretical results.