Reconstruction of Planar Cam Profile Function and its Follower Displacement using B-Spline Curve based on Inverse Subdivision Method and Theory of Contact Relations - Application to Cam Mechanism of Oscillating Follower with Roller

Abstract

For controlling the precision of a manufacturing planar cam mechanism, one can base on a set of digital points
measured on the manufactured cam profile by a coordinate measuring machine (CMM). Issued from this set of
discrete digital points and by applying the well-known B-Spline least squares approach, one can reproduce the
cam profile function. The given cam profile function and the theory of contact relations between cam and its
follower enable us to deduce the displacement law of the follower and its derivatives. This paper presents a new
method for reconstruction of a planar cam profile function from a set of digital points measuring on CMM
machines, using B-Spline curve based on inverse subdivision method and theory of contact relations. An
application to cam mechanism of oscillating follower with roller will be presented. To verify the feasibility and
the accuracy of the proposed inverse subdivision method, a comparison between B-Spline least squares
approach and inverse subdivision has been realized. The method possesses an acceptable accuracy and spends
less time of calculation