Analysis of Errors in the Double Hooke Joint

Abstract

A double Hooke joint consists of two properly connected single Hooke joints for the purpose of transmitting rotation with a uniform angular velocity ratio. Previous kinematic analyses [1, 2, 3] have dealt with Hooke joints of perfect or ideal configuration, viz., in which pertinent axes intersect and are perpendicular. With real Hooke joints the manufacturing errors (which include tolerances) produce axes that do not intersect and are not perpendicular. The present analysis [4] investigates the effects of such departures from the ideal for the case of the double Hooke joint. It considers their effect on the mechanism’s movability, and studies their influence on the displacement, velocity, and acceleration relations between input and output shafts. The problem is solved by matrix methods: displacement relations are derived for the ideal double Hooke joint, after which the effects of small dimensional errors are considered as perturbations from the ideal values. The analytical expressions allow the variations in velocities and accelerations to be obtained by differentiation.