Development of a Seven Degrees of Freedom Crane with Three Wires (1st Report)

Inverse Kinematics of the Crane

Abstract

A 7 d. o. f. crane with three wires is proposed for automatic heavy parts assembly. The crane can control not only desired position but also orientation of a suspended object. The position and orientation control method of the crane is discussed under a static condition. By solving the simultaneous equations given by the geometrical constraints of the wire lengths and force constraints of gravity, the kinematics is calculated. Since the equations are non-linear, Newton Raphson method is used. The kinematic characteristics of the crane is analyzed and the relationship between the desired orientation and the shape of the object is obtained. Redundancy of the crane is used to minimize the maximum value among the three tensions of the wires. The algorithm of the inverse kinematics is proposed and experimental results using a prototype crane prove the verification of the algorithm.