支链布局对重力场下3-PRS并联机构静柔度的影响分析
Analysis on the Influence of Arrangement of Limbs on Compliance of a 3-PRS Parallel Mechanism with Consideration of Gravity

研究了支链布局对重力场下3-PRS 并联机构静柔度的影响．首先通过分别构造静力及静变形在操作空间与 关节空间之间的映射模型，将切削力/力矩、运动部件重力及支链分布重力引起的变形映射到末端，进而借助线性叠 加原理构造系统的静柔度模型；然后建立子装配体在各自局部坐标系中定义的柔度系数与界面柔度系数间的映射模 型；最后，在利用有限元软件验证所建立静柔度模型正确性的基础上，研究机构末端重力引起的变形及末端静柔度 随支链布局不同的变化规律．研究结果表明，全对称布局的3-PRS 并联机构具有较好的抵抗重力和外载荷的能力， 为该类装备的设计提供了理论依据．
With consideration of gravity，the analysis on the influence of arrangement of limbs on the compliance of a 3-PRS parallel mechanism was conducted．By formulating the relationship of the external wrench(deflection of the platform)in the operation space and the forces(compliances)in the joint space，the deformations induced by the cutting force/moment，the gravity of moving components，and the distributed gravity of all limbs were mapped into the deflection of the platform．The compliance model of the whole system was then achieved by means of the linear superposition． Subsequently，the expression of the compliance coefficients at the interfaces in terms of those of the subparts within a limb defined in their own local body-fixed frames was derived．The effectiveness of the proposed modeling approach was verified by the FEA software at a typical configuration，based on which the variations of the deformations caused by the gravity and the compliances of the platform with different arrangements of limbs were investigated．The results show that the fully symmetrical 3-PRS parallel mechanism better resists the gravity and the externally applied wrench imposed upon the platform，which provides a guideline for the design of the mechanism