An analysis of the inverse kinematics for a 5-DOF manipulator

Abstract

This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systemically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.

Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

“…Although the unconstrained direction is fixed with respect to the environment in several methods, 15,16,17,20 the direction is absolutely fixed, and the user cannot change it. Since the unconstrained direction is dependent on the task and environment, the direction should be variable.…”

“…In the former approach, for example, refs. [15][16][17]20], one of the kinematic equations is neglected, and the remaining five simultaneous equations are solved. However, the derived solution does not satisfy the neglected kinematic equation, if the given set of χ i is kinematically unreachable by the manipulator.…”

“…For the Pioneer 2 arm, several researchers have tackled to obtain closedform solutions and to identify singular configurations. 16,17,18 Wang and Ishimatsu 19 analyzed the kinematics of a 5-DOF prosthetic arm that has a special shoulder mechanism. Wang 20 analytically solved the inverse kinematics of a 5-DOF arm attached to an amusement robot to identify the reachable position and orientation of the arm 1 .…”

Optimization Approach for Inverse Kinematic Solution

“…[8] proposed inverse kinematic solution on the basis of quaternion transformation. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have proposed application of quaternion algebra for the solution of inverse kinematics problem of different configurations of robot manipulator. [35] presented a quaternion method for the demonstrating kinematics and dynamics of rigid multibody systems.…”

“…[35] presented a quaternion method for the demonstrating kinematics and dynamics of rigid multibody systems. [34] presented analytical solution of 5-dof manipulator considering singularity analysis. [11] presented quaternion based kinematics and dynamics solution of flexible manipulator.…”