Kinematical Analysis of an Articulated Mechanism

TL;DR

This paper derives kinematic equations for an articulated mechanism with two bars and a disk, performs numerical experiments, and discusses the inversion of rotation sense and deceleration during a 90-degree turn.

Contribution

It provides new mathematical expressions for the kinematics of a specific articulated mechanism and compares constant versus variable angular velocity scenarios.

Findings

Inversion of linking bar rotation sense observed

Deceleration begins during the 90-degree turn

Numerical results align with theoretical predictions

Abstract

The purpose of this work is twofold: to present mathematical expressions for the kinematics of an articulated mechanism and to perform numerical experiments with the implemented code. The system of rigid parts is made of two slender bars and a disk. In the original configuration, a constant counterclockwise rotation rate is imposed on the disk. In the modified version, this angular velocity varies linearly with the rotation angle to produce an average rate that is nearly the same as the constant case. Angles, velocities and accelerations are analyzed for a 90-degree turn of the disk. The numerical solutions show the inversion of the linking bar sense of rotation along with the start of deceleration for both bars. The paper and pencil solution of the original problem that may lead to a wrong conclusion is explained. Equations are derived from first principles and the code is placed under version control. Those in charge of vector dynamics courses may find it useful as a project-based learning activity.