Multibody System Dynamics 11: 127–145, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 127 Tripod and Ball Joint Automotive Transmission Kinetostatic Model Including Friction J.-P. MARIOT 1 , J.-Y. K’NEVEZ 2 and B. BARBEDETTE 1 1 Groupe Composites et Structures Mécaniques, Université du Maine, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France 2 Laboratoire de Mécanique Physique, Université de Bordeaux 1, CNRS UMR 5469, 351 Cours de la Libération, F-33405 Talence Cedex, France (Received: 9 September 2002; accepted in revised form: 18 December 2003) Abstract. This paper deals with a mechanical model of an automotive transmission consisting of a plunging tripod joint close to the gearbox and a ball joint close to the wheel. Both joints are connected by an intermediate shaft. The ball joint is modelled as a constant velocity (CVJ) and frictionless joint. Due to the plunging movement, the tripod joint is not a true CVJ but may be modelled as a perturbed CVJ. To avoid numerical solutions, approximated analytic kinematical equations are derived. Then, it is shown that for a constant input velocity, dynamical effects due to the tripod joint are negligible versus static effects. Accordingly, an inverse kinetostatic model with a constant input velocity and a constant output torque is introduced. Friction between the rollers and the tulip ramps and between the rollers and the trunnions is modelled using a viscous or a Coulomb approach. For viscous friction, analytic expressions of forces and torques are provided and numerical simulations are presented to validate these results. For Coulomb friction only numerical results are available. In particular, it is shown that viscous friction alone cannot generate shudder vibrations. Key words: multibody dynamics, tripod joints, automotive transmissions, shudder, viscous friction, Coulomb friction. Nomenclature R 0 = absolute frame of reference with origin O R 1 = tulip frame with origin  R 2 = tripod frame with origin at tripod centre I R3/R6 = 3/6-fold frequency vibration (3/6 times that of input velocity) 0 A 1 = orientation matrix of frame R 1 with respect to frame R 0 1 A 2 = orientation matrix of frame R 2 with respect to R 1 ϕ, ϕ ± = ϕ ± 2π/3 = input angles (gearbox) θ , θ ± = θ ± 2π/3 = output angles (wheel) ψ , δ = orientation angles of the intermediate shaft with respect to R 1 C 1 , C 2 , C 3 = roller positions F , F 1 , F 2 , F 3 = orthoradial force components in the tripod plane Fr 1 , Fr 2 , Fr 3 = friction force components parallel to tulip axis Ft 1 , Ft 2 , Ft 3 = friction force components parallel to tripod axis R 1 , R 2 , R 3 = force components along the intermediate shaft N 1 , N 2 , N 3 = orthoradial force components in the plane orthogonal to the tulip axis