改进Delta并联机构运动可靠性分析

Kinematic Reliability of Improved Delta Parallel Mechanism

运动精度是评价机构质量的重要考核指标。以往并联机构运动精度分析中,往往不考虑输入误差的随机性,造成评价结果不准确。首先应用齐次坐标变换,推导了改进Delta并联机构的位置反解公式。基于位置反解和一阶泰勒展开,建立了包含机构尺寸误差、转动副间隙误差和驱动误差的机构位置误差计算模型。利用该误差模型,考虑各个原始输入误差的随机性,推导了机构运动可靠性数学模型,给出了评价机构运动可靠性高低的量度和计算方法。运动可靠性是机构运动精度高低的更本质的衡量指标。运动可靠性分析是机构优化设计和误差补偿的基础。

Kinematic accuracy is an important index to evaluate the quality of mechanisms. Kinematic accuracy analysis of the parallel mechanisms in previous study ignores the randomness of each input error component, so the conclusions are imprecise. Using the homogeneous transformation, inverse kinematics of the improved Delta mechanism is calculated. Based on the inverse kinematics and the first order Taylor approach, error model considering original errors from kinematic parameters describing the mechanism＇s geometry, clearance errors of revolving pair and driving errors are presented. Based on the error model, considering the randomness of every input error components, math model of kinematic reliability of the improved Delta mechanism is deduced; and the evaluation and calculation methods of kinematic reliability of the mechanism are put forward. Kinematic reliability is the key factor of evaluate kinematic accuracy of mechanism; and kinematic reliability analysis provides the foundations for optimum design and error compensation of the mechanism.