On the torque transmission by a Cardan-Hooke joint

Kinematics and dynamics of a Cardan-Hooke joint are investigated. Kinematic analysis is based on the kinematic chain rule for angular velocity vectors. Dynamics of the Cardan-Hooke joint is analyzed by means of the Lagrange equations of the second kind. The Cardan-Hooke joint is analysed under varying operating conditions, that is, it is assumed that the input shaft has variable angular velocity. Two cases are considered: (1) the driving yoke plane coincides with the plane of the shafts; (2) the driving yoke plane is normal to the plane of the shafts. An expression for torque transmission in a Cardan-Hooke joint in varying operating conditions was developed. The expression contains terms representing inertia of the shafts and the cross of the Cardan-Hooke joint. Theoretical considerations are accompanied by a numerical example.