Calculating conjugate cam profiles by vector equations

Abstract

This paper presents an analytical approach for determining the profiles of conjugate disc cams. For a conjugate cam mechanism, its two normal lines through the points of contact and the line of centres must always intersect at a common point, which is an instant centre. On this basis, the contact points between the conjugate cam and the follower can be determined according to the locations of instant centres and follower position. The cam profiles, the paths of the cutter and the pressure angles can then be expressed in the form of parametric vector equations. For various types of conjugate cams, the equations for such expressions are formulated, and examples are provided to illustrate the approach. The procedure is especially simple to program.

A Convenient and Inexpensive Quality Control Method for Examining the Accuracy of Conjugate Cam Profiles

“…For easy reference, the analytical expressions derived by Wu (2003) are provided in this section. For the conjugate cam mechanism shown in Fig.…”

“…1, the two normal lines through the points of contact and line of centers must always intersect at the instant center I 23 (Wu, 2003), where "I" denotes the instant center and subscripts indicate the related links. For simplicity, in the following, the frame will be consistently numbered as 1, the cam as 2 and the follower as 3.…”

“…For simplicity, in the following, the frame will be consistently numbered as 1, the cam as 2 and the follower as 3. By labeling instant center I 23 as Q and O 2 Q = q, the parametric vector equations of the cam profile coordinates are (Wu, 2003) …”

“…Being a high-value-added product, a conjugate cam mechanism consists of a pair of disk cams that their profiles must be mutually conjugate to contact their respective follower. The conjugate cam mechanism is therefore a positive-drive mechanism (Wu, 2003;Rothbart, 2004;Norton, 2009) that can eliminate the use of return springs. As a benefit of positive-drive, the conjugate cam mechanism can ensure the contact between the cam and the follower roller with lower contact stresses between them.…”

“…In other words, reasonably designed conjugate cam mechanisms are especially suited to high-speed applications. However, since a conjugate cam mechanism is a so-called kinematically overconstrained arrangement (Wu, 2003), to ensure its movability condition and its ability to run without backlash (Rothbart, 2004;Norton, 2009), its cam profiles must be accurately designed and machined. The machined cams must then be carefully examined to check whether their profile errors fall within a specified tolerance range in order to achieve high quality and performance of the mechanism.…”