Certain manufacturing industries, including the semiconductor industry, are now moving toward very high-speed machinery requiring very small yet precise motions. The total path of a coupler point on harmonic motion-generating linkages, with relatively small input cranks, has been shown to be an approximate ellipse. Such linkages have been described to possess superior performance qualities for high speed machine application. Two special cases of the elliptical path are circular and linear paths. An investigation of the kinematic equations, which govern the motion of a coupler point, reveal the nonexistence of such exact paths, prompting the two theorems with proofs forwarded herein. Linkages are synthesized in an effort to find coupler points which trace “near-circle” and “near-straight-line” entire paths. Some interesting results are obtained in studying the motion behavior of coupler points on such linkages.

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