Error model and geometric error sensitivity simulation of new 2UPR/UPS/UP mechanism
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摘要:
研究推导2UPR/UPS/UP+AC摆混联机构的解析反解，并以2UPR/UPS/UP为研究对象，系统阐述单关节误差模型和支链误差模型，并给出相关的几何误差源；建立被动误差、动平台位姿误差与各支链运动副误差源之间的误差映射模型，并基于机构误差模型进行各运动副误差源的误差灵敏度仿真分析. 研究成果可为基于2UPR/UPS/UP并联机构的五自由度混联机器人工程设计提供运动副误差分配及精度设计的理论支撑，同时为其他混并联机构的误差建模和灵敏度分析提供借鉴.
Abstract:The analytical inverse solution of 2UPR/UPS/UP+AC pendulum hybrid mechanism was derived. With 2UPR/UPS/UP mechanism as the research object, the single-joint error model and branched-chain error model were systematically expounded , and the related geometric error sources were given. The error mapping models among the passive error, the pose error of the moving platform and the error sources of the motion pairs of each branch chain were established, and the error sensitivity of the error sources of each motion pair was simulated based on the mechanism error model. The research results can provide theoretical support for motion error distribution and precision design of 5-DOF hybrid robot engineering design based on 2UPR/UPS/UP parallel mechanism, as well as reference for error modeling and sensitivity analysis of other hybrid mechanisms and parallel mechanisms.
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Key words:
- 5-DOF hybrid robot /
- parallel mechanism /
- error model /
- error sensitivity analysis /
- passive error
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表 1 AC摆的DH参数
Table 1. DH parameters of AC pendulum
连杆 ${\alpha _{i - 1}}$ ${a_{i - 1}}$ ${d_i}$ ${\theta _i}$ 变化范围 1(D) 0º 0 m ${\theta _1}$ $\left[ {- {\text{π} },{\text{π} } } \right]$ 2(E) 0º 0 0 ${\theta _2}$ $\left[ {-{\text{π} } /2,{\text{π} } /2} \right]$ 3(F) 90º 0 n −90º 
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表 2 UPR支链几何误差定义
Table 2. Geometric error definition of UPR branch chain
几何误差源 误差含义 备注 Δa1=
(Δxa1, Δya1, Δza1)U1副近架轴线位置误差 在系{O}下 ΔθA1x =
(ΔθA1xx, ΔθA1xy, ΔθA1xz)U1副近架轴线姿态误差 在系{O}下 Δa1x=
(Δxa1x, Δya1x, Δza 1x)U1副近架轴线与远
架轴线间位置误差在系{A1x}下 ΔθA1y =
(ΔθA1yx, ΔθA1yy, ΔθA1yz)U1副远架轴线姿态误差 在系{A1x}下 Δa1y=
(Δxa1y, Δya1y, Δza1y)U1副远架轴线与支
链轴线间位置误差在系{A1y}下 Δl1=
(Δxl1, Δyl1, Δzl1)支链移动方向误差 在系{A1y}下 ΔθB1y =
(ΔθB1yx, ΔθB1yy, ΔθB1yz)R1副旋转轴线姿态误差 在系{A1y}下 Δb1=
(Δxb1, Δyb1, Δzb1)动平台铰链点B1的位置误差 在系{C}下
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表 3 并联机构杆长参数
Table 3. Rod length parameters of parallel mechanism
参数 ${l_1}/{\rm{mm}}$ ${l_2}/{\rm{mm}}$ ${l_3}/{\rm{mm}}$ Min 881 881 881 Max 1481 1481 1481
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