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针对以2R1T对称并联机构中3-RPS并联机构为核心的机械腿,基于矩阵全微分理论,建立了机构位姿误差模型.通过数值仿真得知,相对机构误差对动平台X与Y向的影响,其对Z向的影响更大,将产生较大误差,达到0.308 mm;对应的Rodrigues参数中Φ2误差相对于Φ1变化较大,达到7.1×10-5,参数Φ3保持为零.一些结构误差由于使末端位姿发生明显变化,在制造与装配工艺性方面应相应加强;在驱动杆件误差发生变化时,末端位置Z轴参数变化较大,在0.5mm范围内变化,末端姿态参数Φ2的误差分量约是相应Φ1变化值的2倍;各项误差导致的动平台位置误差呈非线性趋势变化,但变化较小,可近似为线性变化,可用软件方法进行补偿.
Aiming at the mechanical legs with 3-RPS parallel mechanism as the core in 2R1T parallel mechanism, the pose error model of mechanism is established based on the matrix differential theory.The numerical simulation shows that the influence of relative mechanism error on the X and Y directions , Which has a greater influence on the Z direction and will result in a larger error of 0.308 mm. The Φ2 error in the corresponding Rodrigues parameter varies greatly from Φ1 to 7.1 × 10-5, and the parameter Φ3 remains at zero. Some structural errors Due to the obvious change of posture, the Z-axis parameters should be changed greatly in the range of 0.5mm when the error of the driving rod changes. The tip attitude parameter Φ2 The error component is about 2 times the corresponding value of Φ1. The position error of the moving platform caused by each error shows a nonlinear trend, but the change is small and can be approximated as a linear change, which can be compensated by software method.