Numerical Iterative Algorithm for Solving Kinematics and Dynamics of Under-actuated Mechanisms with Flexible Joints

doi:10.3901/JME.2018.13.066

Abstract

Abstract: The kinematic and dynamic constraints of under-actuated mechanism are incomplete and its movement is uncertain. The elastic reaction of flexible joints involved in an under-actuated mechanism can make up for the incompleteness of dynamic constraints in a way, but the kinematics and dynamics equations are still unsolvable. To solve this problem, a planar 2-DOF under-actuated mechanism with a flexible joint, as an example, is analyzed. A numerical iterative algorithm is proposed to solve the kinematics and dynamics. Based on the kinematics model and dynamics model, the initial conditions of all the components and the motion law of the active joint are given. In the course of numerical iteration, considered the theory that velocity and acceleration is the same in an extremely brief period, the motion laws of all the components and the driving force/torque of the active joint can be obtained. Based on Matlab programming, the kinematics and dynamics equation is solved, and the relationship between the flexible joint stiffness of the flexible joint and the driving torque is analyzed. Also, the equations solution influenced by the flexible joint stiffness is analyzed. This numerical iterative algorithm will break through the bottleneck of the further study of this kind of mechanisms to a certain extent.

Key words: flexible joint, iterative algorithm, kinematics and dynamics, under-actuated mechanism

CLC Number:

TH112

ZHANG Jianjun, DU Chuncui, YANG Gaowei, LI Weimin. Numerical Iterative Algorithm for Solving Kinematics and Dynamics of Under-actuated Mechanisms with Flexible Joints[J]. Journal of Mechanical Engineering, 2018, 54(13): 66-72.

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