A Multibody Loop Constraints Approach for Modelling Cam/Follower Devices: Application in Mobile Robotics

Abstract

This paper proposes a formulation for modelling mechanisms with cam/follower type of contact using a multibody approach in relative coordinates. The proposed approach is inspired from the wheel/rail contact model developed in (Fisette, Samin, 1994) but in the present case, possible intermittent contact between the cam and the follower is considered, for generality purposes. Loop kinematic constraints are introduced to satisfy tangent and punctual contact as long as the bodies lean against each other. The effective presence (or not) of the contact is governed by the sign of the normal constraint force which can be computed thanks to the Lagrange multipliers technique. The above-mentioned option to kinematically constraint the bodies in their “contact phase” unavoidably leads to shift from one model to another when a contact disappears (or conversely reappears). Indeed, this increases (or decreases) the number of degrees of freedom of the current system. The control of the variable partitioning is thus absolutely necessary and is all the more complex that practical applications can contain several pairs of bodies in intermittent contact. As regards the applications, a comparison with another multi-body formalism and an experimental validation are discussed at first. Then, the modelling and simulation of universal wheels of an omnimobile mobile robot, developed in our Division, are proposed. The latter model represents a quite original application of the proposed multibody formulation. Computations are now in progress to analyse the complete behaviour of the robot, including control performances.

Optimization and synthesis of a cam-linkage mechanism with a swing follower with variable pivot

“…The orientation of the slide guide rail (6) is adjustable. When required, the drive adjusting motor (10) rotates to drive the lead screw (7) through the coupler (9), which alters the position of the lead screw slider (8). A position change of the lead screw slider (8) will change the orientation of the rectangular slide guide rail (6).…”

“…Cardona and G eradin 6 investigated the kinematics and dynamics of mechanisms with cams. Fisette et al 7 extended this work to model cam systems using multibody system methodologies. Based on multibody systems, Cardona et al 8 proposed a methodology to design cams for motor engine valve trains using a constrained optimization algorithm.…”

“…Fisette et al. 7 extended this work to model cam systems using multibody system methodologies. Based on multibody systems, Cardona et al.…”