Harmonic Linearization Method for Computing the Motions of a Specific Type of Three-Joint Arms

Abstract

Abstract The paper presents a three-joint arm that has two translational fifth-class kinematic pairs and a rotational one. The first two kinematic pairs are axially orthogonal, while the second and the third one are axially parallel. Such robots find use in machinery handling for arc welding. Systems of three nonlinear second-order differential equations were obtained to describe the motions of this arm. As it was necessary to assess the moment of load emerging on the control-drive shaft, the external generalized forces were reduced to a corresponding generalized coordinate. Harmonic linearization of nonlinearities was applied to analyze the arm system. This method can be used to fine the core properties of the system (frequency, amplitude, and phase of the oscillations; dependence of the form of nonlinearities or on the parameters of the linear part; etc.) without studying the transient.Ratios were obtained to find the parameters of natural oscillational motion occurring in such arms. These rations can be used to design and set up such an arm. The finding is that where the system of equations describing the motion of such an arm (including the drive motion equations) contains no prominent nonlinearities, these rations are a system of two algebraic frequency equations: a sixth-degree one and a fifth-degree one.