Abstract
Cam mechanisms have been applied in a wide variety of machines and mechanical devices. Up to now, cams still play an important role in the mechanical industry and cannot be superseded. Because cams are irregular-shaped mechanical components, their profiles cannot be accurately machined with relative ease. Therefore, the cam profile tolerancing and error inspection become important tasks in the design and manufacture of precision cam mechanisms. The purpose of the mechanical error analysis of the cam mechanism is to establish the theoretical correlation between the tolerance (or deviation) of each design parameter and the follower motion deviation. That is, the analysis of mechanical errors is a fundamental of tolerance design of precision cam mechanisms. The main purpose of this dissertation is to present a relatively simple and systematic analytical method to perform the mechanical error analysis of planar cam mechanisms. This analytical method can also be extended to apply to the optimal tolerance allocation for planar cam mechanisms and to the profile error inspection of disk cams and conjugate cams. Firstly, by employing the concept of equivalent linkage and the derived correlation between the radial-dimension errors and the normal-direction errors of the cam profile, an analytical method, called the equivalent linkage method, is developed to analytically predict the kinematic errors of the follower caused by the deviation in each design parameter of planar cam mechanisms. This method can effectively and systematically perform the mechanical error analysis of planar cam mechanisms to obtain the displacement, velocity, and acceleration error equations of the follower motion. Here, this method is validated through analyzing an eccentric circular cam mechanism whose exact solution is available, and also examined through evaluating the profile error of an exaggerated case whose relatively large profile error is caused by adopting an incorrect follower motion program. Then the method is illustrated through analyzing the mechanical errors of all four types of commonly used disk cam mechanisms and a planar cam-follower type pick-and-place device. Secondly, by incorporating the equivalent linkage method and the concept of design for manufacture and assembly (DFMA), this study develops a procedure of optimal tolerance allocation for planar cam mechanisms. The objective of this optimal procedure is to maximize the manufacturability and assembility of the cam mechanism while maintaining acceptable kinematic accuracy of the follower motion. This optimal procedure is illustrated by allocating the tolerances in a planar cam-follower type pick-and-place device. Furthermore, in order to inspect the profile deviations of disk cams, a direct and concise analytical method for dealing with the coordinate measurement data obtained from a coordinate measuring machine (CMM) is proposed. The method is based on the derived correlation between the radial-dimension errors and the normal-direction errors of disk cam profiles. To verify this method, an experiment of inspecting a pair of conjugate disk cams was conducted. The experimental results obtained from the proposed method were compared with those obtained by using the Hermite interpolation method. It shows that this method is accurate and more efficient for dealing with the coordinate measurement data to inspect the profile errors of disk cams. This study also demonstrates how to use a special measuring fixture to measure the conjugate condition of an assembled conjugate cam mechanism so as to indirectly evaluate the deviations of conjugate cam profiles; for such an indirect measurement method, the only required measuring instrument is a dial indicator. For a conjugate cam mechanism being examined, by employing the equivalent linkage method, the correlation between the conjugate condition variations and the cam profile errors can be derived analytically. Based on the correlation, conservative criteria for qualify control of assembled conjugate cams are proposed. This indirect measurement method is particularly suitable for the quality control in mass production of conjugate cams. Furthermore, if a pair of master conjugate cams with known profile errors is additionally available, through the measured conjugate condition variations of a pair of assembled conjugate cams consisting of one master cam and the other being an inspected cam, then the profile errors of each individual inspected cam can be estimated. This indirect measurement method is illustrated by two examples. Also, a pair of conjugate cams were examined by the method and also measured using a CMM to test the accuracy of the method. It shows quite a good agreement between prediction and experimental results. In summary, this dissertation provides simple and efficient means for analyzing the mechanical errors, for allocating the tolerances, and for examining the profile errors of various types of disk cams and conjugate cams.