Tripod Joint Research Articles

Dynamics of an automotive transmission consisting of a tripod joint and a ball joint. A symbolic approach

The present paper deals with the zero friction dynamics of an automotive transmission consisting of an inboard ball joint close to the wheel and an outboard tripod joint close to the gearbox, connected by an intermediate shaft. The ball joint is a constant-velocity joint (CVJ) whereas the tripod joint is not. In the idealized case of an intermediate shaft of infinite length, the tripod joint behaves like a CVJ and has the following properties: the input and output torque are equal, the transverse forces generating the output torque are equal and there are no shudder vibrations or inertial shaft effects. For a real transmission with a finite-length shaft, deviations from constant-velocity (CV) properties are due to tripod joint angle variation which causes static and dynamic perturbations; these perturbations are expressed symbolically using first-order approximations in terms of tripod joint angle and ratio of shaft length to tulip radius. For most of the front drive cars equipped, the angle of the tripod joint remains close to 0.1 rad; considering a constant input torque at a 100rad/s input velocity, the perturbations are found to be less than 3 per cent for the driving forces when compared with the CVJ.

Kinematics of transmissions consisting of an outboard ball joint and an inboard generalized tripod joint

This paper presents the kinematics of transmissions consisting of an outboard ball joint close to the wheel and a tripod joint close to the gearbox. Emphasis is placed on the intrinsic properties of the tripod joint owing to the orthogonality between the tripod legs and the intermediate shaft. In particular, it is shown that the roller-tripod centre distances are available analytically with a mere dependence on the intermediate shaft rotation angle and the joint angle. For the whole transmission, the kinematics reduces to two non-linear equations with the upper two angles as unknowns. Following numerical simulations, an approximate solution is proposed for evaluating the departure from constant velocity behaviour. A generalized joint derived by bending the tripod legs and the tulip ramps is introduced, and the influence of these geometrical modifications on the roller-to-tripod centre distances is shown. Optimization techniques based on evolutionary algorithms have been introduced for minimizing the generation of vibrations caused by roller-to-tripod movements. In many of the examples shown, geometric approaches have been used both for illustration and calculation.

Kinematic and Dynamic Analyses of the Tripode Joint

This paper is concerned with an application of multibody techniques to the dynamic analysis of the tripode joint. The purpose of the mathematical model developed is the computation of all the constraint forces. In fact, the results of this investigation are preliminary for a study on the influence of geometry and inertia design parameters on the noise and vibrations caused by the joint.

On the Motion Characteristics of Tripode Joints. Part 2: Applications

The theory developed in Part 1 has been applied to the determination of motion characteristics of two typical types of shaft couplings involving tripode joints. An ideal case of an exact constant-velocity coupling is first described and analyzed. The remainder of the paper focuses on a practical shaft coupling of the tripode-Rzeppa combination which is widely used in front-wheel drive vehicles. The results demonstrate that the displacement equation of this combination is a fourth-order polynomial in the tangent of the output crank angle, and this coupling does not provide a true constant-velocity joint, but rather an approximate one. Parameters affecting the velocity fluctuation and their influences are presented. In addition, it is found that there exists a definite phase lag of thirty degrees between the displacement and velocity curves at all times on the output shaft. Whenever possible, numerical results for the motion characteristics of the joint and its components are illustrated by computer-plotted graphs, which may also offer some insight into the behavior of the tripode joint.

On the Motion Characteristics of Tripode Joints. Part 1: General Case

This paper is concerned with the analytical investigation of the motion characteristics of tripode joints with general proportions and arbitrary position of shafts. It provides a rigorous proof that the tripode joint is not a true constant velocity joint except in ideal cases, and this is due to the inherent orbital motion of the output spider shaft. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented. From this general analytical study, some insights into the behavior of the tripode joint are observed and interpreted.

Kinematic Properties of Tripode (Tri-pot) Joints

The geometry of tripode (also called tri-pot) joints or shaft couplings is simplified by folding one side onto the other, and the kinematic properties are obtained. Due to a built-in orbital motion, a tripode joint cannot be used alone between two shafts of fixed axes; therefore it cannot directly be compared with a typical CV (constant-velocity) joint. Yet it is shown that: (a) if its shafts are kept parallel to a fixed plane a tripode joint transmits equal rotations as other CV joints do; (b) if one shaft axis is fixed and the other shaft axis has a fixed point, input and output angular velocities slightly differ, with a cycle of three times shaft speed; (c) to transmit rotation between two shafts of fixed axes, a tripode joint must be incorporated with another tripode or CV joint or a mechanism. In this case deviation between input and output angular velocities can be made very small or even nil.