Optimization of Cam Mechanisms
1. 1 Preliminary Concepts A cam mechanism is a mechanical system consisting of three basic components: a driving element, called the cam; a driven element, termed the follower; and a fixed frame. Sometimes, an intermediate element is introduced between the cam and the follower with the purpose of improving the mechanism performance. This element is called the roller because function is to produce a pure-rolling relative motion be tween the cam and the follower. The purpose ofa cam mechanism is the transmission of power or information. In applications concerning power transmission, the main good to be transmitted is force or torque; in applications ofinformation transmission, the main good transmitted takes the form of motion signals. Most modern appli cations of cam mechanisms, to be described shortly, are of the former type. Cam mechanisms used for information transmission were traditionally found in measuring instruments. With the advent ofmodern microprocessor-based hardware, this typeof application is becoming less common. Nevertheless, cam mechanisms are still used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, computers, printing presses, food-processing equipment, internal combustion engines, control systems, and photographic equipment (Prenzel, 1989). In the design of cam mechanisms, the engineer performs several activities, namely, task definition, synthesis, analysis, optimization, and dynamic simulation. These tasks do not always follow this order. In fact, some loops may appear in the foregoing tasks, such as those illustrated in Fig. 1. 1. 1.
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Cam and Follower
THE DISPLACEMENT PROGRAM
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3-4-5 polynomial motion absolute value acceleration analysis axis base circle base radius calculated cam disk cam mechanism cam plate cam profile Cartesian coordinates centroid chain rule Chapter coefficients computed Computer-Aided Design constraints contour cubic splines cusps cycloidal motion cylindrical cam defined denoted determined discussed disk cams displacement program equations Example expression foregoing formulas function given by eq graphics hence inertia matrix integrals introduced ISBN kinematic kinematic pair knife-edge follower line integrals machine tool maximum methods minimum value Moreover motion program namely normal motion numerical obtained optimization optimum Oravas oscillating flat-face follower oscillating roller-follower parameters pitch curve planar plot polar coordinates polygon position vector pressure angle produce quartic equation radius of curvature return phase rise phase roller roller-follower Section shown in Fig sides of eq Solid Mechanics Subsection Substitution of eq surface surface integrals synthesis tangent translating flat-face follower translating follower translating roller-follower type of cam velocity yields zero