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首页> 外文期刊>Journal of Mechanical Design >Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators
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Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators

机译：大型三腿并联机械手直接位置分析的解析形式解

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A wide family of parallel manipulators (PMs) is the one that groups all PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen.
机译：广泛的并联操纵器（PM）系列是将所有PM分为三条腿，其中的腿成为运动链，该运动链由与被动棱镜对（P）或被动旋转对串联的被动球形对（S）组成（R）执行器锁定时。当致动器被锁定时，由这些机械手生成的结构的拓扑为十种。这些拓扑中的两个是SR-2PS拓扑（一个SR分支和两个PS分支）和SP-2RS拓扑（一个SP分支和两个RS分支）。本文提出两种算法。第一个确定SR-2PS结构的所有组装方式。第二个确定SP-2RS结构的所有组装模式。所提出的算法可以不经修改地应用，以解析形式解决当执行器锁定时产生SR-2PS结构或SP-2RS结构的所有并联操纵器的直接位置分析（DPA）。特别是，写出了两种通用结构的闭合方程，一种是SR-2PS型，另一种是SP-2RS型。确定了两个方程组的消除子，并给出了求解程序。最后，建议的程序适用于实际案例。这项工作证明（i）成为SR-2PS结构的任何PM的DPA解决方案最多为八个，以及（ii）成为SP-2RS结构的任何PM的DPA解决方案最多为16。

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