Position and velocity analyses of the tripod joint with aspherical rollers

The paper addresses the kinematics of a type of tripod joint that has seen application over the past two decades in the automotive industry, due to its anti-shudder features. The joint encompasses three rollers externally delimited by axisymmetric non-spherical surfaces. The rollers run on tracks machined on one of the connected shafts. Each roller has a cylindrical inner surface that is in contact, theoretically along a circle, with the spherical ending of a trunnion extending from the other shaft. The paper solves for the first time in polynomial form the position analysis of this type of joint. Then, after pointing out that a tripod joint does not have an instantaneous transmission ratio, the paper addresses the first-order kinematics of the joint. As a further original result, the paper demonstrates that the analyzed tripod joint, when connected in series to a ball non-plunging constant velocity joint, gives rise to a three-shaft driveline which is strictly homokinetic if the axes of the terminal shafts are parallel. Numerical examples show application to case studies of the procedures proposed to solve the position and velocity analyses.