球面四杆机构综合的极射赤面投影方法

空间机构的分析综合比较困难,以正投影为基础的图解法,由于图上不能反映空间真实角度,作图烦琐,多年来一直未得到发展1,2];解析法涉及较高深的数学,难为工程师掌握和应用。BAGCI利用极射赤面投影为空间机构的分析和综合开辟了新的途径3],它将空间问题在基圆平面内直接进行作图,显示了该法的简便性。本文是在BAGCI的工作基础上用Wulff网作图度量,较其更加简便、容易掌握。机构的解析表达,可用图解结果以球面三角公式直接写出,不需推导与证明。本文利用极射赤面投影对球面四杆机构综合的转动极与等视角定理、相对运动的转换等原理进行了讨论,并以实例说明这些原理的应用。对图解与计算结果作了比较,说明图解精度可满足工程实际需要。

Stereographic Projection Method for Synthesis of Spherical Four-Bar Mechanisms

Past papers on this subject are quite few. The authors believe such asituation can be understood by first giving a brief sketch of historicaldevelopment before presenting the authors' new contribution. It is not easy to analyze and synthesize spatial mechanisms. Graphicalmethods that are based on orthographic projection cannot give the correctmagnitudes of angles and, moreover, the graphical construction is tedious. Sothey have not been developed for years1,2]. Analytical methods involverelatively advanced mathematics, making them very difficult to be grasped andapplied by engineers. In crystallography, stereographic projection was used to solve spatialproblems quite conveniently. But linear dimensions cannot be convenientlyshown by stereographic projection; thus most engineering situations cannot usesuch projections and "most engineers are unfamiliar with its use" 5]. Ganeand Bagci's papers bring stereographic projection into use in some engineeringfields5, 3,6], thus opening the way to its possible use in other engineering fields. Unfortunately, the powerful tool in the form of Wulff net appeared to beunknown to Bagci, So Bagci's pioneering work was still tedious and diffcult tograsp. Gane used Wulff net but did not deal with spatial mechanisms. This paperl starting from Bagci's work, uses Wulff net to construct graphsand measure from them the data needed for manufacturing. The author'smethod is believed to be simple, intuitive, and easy to grasp. From the authors'graphical solution, with the help of formulas in spherical trigonometry, formulasfor solving spatial mechanism can be directly written down. Comparison of thegraphical results with calculated results indicate clearly that graphical precisionis good enough for engineering purposes.