In this paper, an original equivalent mechanism with parallel linkages is proposed for lost motion behavior analysis and tolerance synthesis of planetary gear train (PGT). The parallel linkages are equivalent in kinematics of PGT to depict the multiple branches of sun-planet-ring gears with a driving link/sun gear and an output platform/carrier, a slider-block with two strokes in the circle curve guide rail of the platform is introduced in each linkage to intuitively express the lag rotation of output platform driven by the parallel linkages under error condition, and the errors are described by the deviations of link lengths. With the mechanism model, the lost motion expression of PGT is explicitly derived and then the tolerance synthesis method is formulated to allocate the optimum tolerances for satisfying the lost motion requirement with the minimum manufacturing cost. The lost motion behavior of PGT was simulated and the tolerances of errors were allocated involving tooth thickness reduction, planet position errors and gear eccentricity errors. The lost motion tests of two PGTs with the allocated tolerances were conducted. The results well agree with the simulations’, which validated the effectiveness of the developed tolerance synthesis method by the proposed mechanism model.

在本文中，提出了一种原始的平行连杆等效机构，用于行星齿轮系 (PGT) 的空转行为分析和公差综合。平行连杆在 PGT 的运动学中等效，以描绘带有驱动连杆/太阳齿轮和输出平台/托架的太阳-行星-齿圈的多个分支，在其圆弧导轨中具有两个行程的滑块。在每个连杆中引入平台，直观地表达出平行连杆驱动的输出平台在误差条件下的滞后旋转，误差用连杆长度的偏差来描述。随着机制模型，明确推导了 PGT 的空转表达式，然后制定了公差综合方法，以分配最佳公差，以最小的制造成本满足空转要求。模拟了 PGT 的空转行为，并分配了误差容限，包括齿厚减少、行星位置误差和齿轮偏心误差。进行了具有分配公差的两个 PGT 的空转测试。结果与模拟结果非常吻合，验证了所提出的机制模型所开发的公差综合方法的有效性。进行了具有分配公差的两个 PGT 的空转测试。结果与模拟结果非常吻合，验证了所提出的机制模型所开发的公差综合方法的有效性。进行了具有分配公差的两个 PGT 的空转测试。结果与模拟结果非常吻合，验证了所提出的机制模型所开发的公差综合方法的有效性。