Mechanism and Machine Theory Vol. 18, No. I, pp. 49-56, 1983 0094-114X[831010049-08503.00[0 Printed in Great Britain. © 1983 Pergamon Press Ltd. SYNTHESIS OF CAM-FOLLOWER SYSTEMS WITH ROLLING CONTACT A. GHOSHt and R. P. YADAV* Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India (Received for publication 20 April 1982) Abstract--The present work deals with the synthesis of cam follower systems with rollingcontact during the rise period of a dwell-rise-dwell return cam. It has been found that the total lift of the follower can not be achieved solely by rolling contact, therefore sliding is permitted for a fraction of the lift. On the basis of minimum work-loss, the respective percentages of contribution by pure rolling contact and rolling cure sliding action have been worked out. I. INTRODUCTION In ordinary cam-follower system sliding also exists at the cam-follower interface. This causes wear of the contact surfaces which is not desirable. Hence rolling action between the contact surfaces may prove to be an ad- vantageous proposition. In the field of cam-follower synthesis with rolling contact some preliminary work has been done by Veldkamp[1]. He has synthesised the cam contour cor- responding to a flat face follower to achieve pure rolling contact. But the applicability of the system proposed by him is limited because the follower motion no longer remains arbitrary and cam should also have oscillatory rotational motion to provide rise and return. In the present work cam-follower systems have been synthesised for rise period of a dwell-rise-dwell cam in view of rolling contact. It has been found that for dwell- rise-dwell return cam the total lift cannot be achieved by rolling contact alone, therefore sliding is permitted for a fraction of the lift. On the basis of minimum work-loss consideration, it can be established that what fraction of the total lift be contributed by rolling contact and what fraction be rolling-cum-sliding contact. 2. ANALYTICAL FORMULATION FOR ROLLING CONTACT Here, for rolling contact the cam and the follower contours will be synthesised. The schematic arrangement is as shown in Fig. 1. It is assumed that two planes, trl and tr2, are rigidly attached to the follower F and the cam C respectively and they lie in the common plane of symmetry of the cam and the follower. For the motion, "cam rolls without sliding on the face of the follower", the centrode in the plane ~r, is the curve C~ and curve C2 in the plane tr2. XOY is the co-ordinate system attached to the fol- lower which is assumed to be fixed. The co-ordinate system xAy is embedded onto the cam and it has the origin at the point A, A being the centre of rotation of the cam. The co-ordinate systems XOY and xAy have the same orientation. (a, b) are the co-ordinates of the fProfessor. CGraduate Student. point A with respect to the fixed axes OX and OY. ~b represents the angle of cam rotation, ~ being taken as positive when measured clockwise. If the point of contact P between the cam and the follower surfaces has the co-ordinates (X, Y) in the reference system XOY and (x, y) in the system xAy, then as per the law of co-ordinate transformation X = x cos r~ - y sin ga + a Y = x sin (~ + y cos ~p + b. O) (2) Now, the relative motion between the cam and the follower can be also achieved through the following motion: Follower is assumed to be fixed, cam rotates as well as the point A translates along a straight line which is parallel to the axis of the follower. The translatory motion of the follower is similar to the required motion of the cam. Let P1 be a point on the follower adjacent to the point P. Since the follower is fixed Vp, = 0 (3) where Vp~ is the velocity of point P1 with respect to the fixed axes XOY. The condition, represented by (3), demands that .~ = 0 (4) and 1? = 0 (5) ,~ and 17 representing the time derivatives of X and Y, respectively. Using (4) and (5) eqns 1 and 2 yield and where x sin $ + y cos ~ = a' (6) - x cos q~+ y sin $ = b' (7) da ., db a' = -:-:-, and ~d'~o 49 MMT Vol.18, No. I--D