建立转向架参数测定试验台几何解析模型与运动学模型，提出一种基于类线性解耦几何解析法与高阶收敛迭代法相结合的混合策略求解并联机构位姿正解。利用类线性解耦几何解析法建立方程组快速求解位姿正解近似值且作为高阶收敛迭代法的初值。以转向架参数测定试验台为例，基于方位特征集理论（Position and orientation characteristics，POC）对该冗余6-DOF机构进行拓扑结构特性分析和运动学结构分析求得位移传输比矩阵r，根据位移叠加性原理建立方程组求得正解初值，进而运用高阶迭代法求解位姿正解。选取圆形周期性轨迹作为该机构运动轨迹，仿真结果表明，几何解析法求得位姿正解误差值不超过0.8%，且混合策略相比Newton-Raphson法迭代次数减少41%，迭代时间缩短23%，满足了试验的实时性要求。试验台回转角刚度试验结果表明：运用装置测量的回转角度值较给定值误差小于0.041 rad，而用提出方法计算回转角度值误差不超过0.019 rad，进一步验证混合策略的有效性与实时性。
Geometric analytical model and kinematic model of test bench for bogie parameters(TBBP) are established. A hybrid strategy(HS) based on geometric analytical method and High-order convergent iteration method for the forward kinematics problem (FKP) of parallel mechanism is proposed. Set the pose value fast obtained by solving the equations built by geometric analytic method as the initial guess of high-order convergent iteration method. Taking the TBBP as an example, based on the theory of position and orientation characteristic(POC) set, the Topological structure characteristics of the redundant 6-DOF parallel mechanism was analyzed. Specific Ratio matrix is acquired by analyzing kinematic structure characteristics of this mechanism. According to Principle of displacement superposition, the initial guess of FKP is gained. This solution is next considered as an initial guess for high-order numerical technique and obtains the answer with a desired level of accuracy. Select circumferential trajectory as the mechanism's motion trail, simulation results shows that compared with given value, error value of the FKP computed by geometric analytic method is less than 0.8%. And comparing with Newton-Raphson(NR) method, iteration number of HS is reduced by 41%, iteration time is reduced by 23%. The real-time demand of the test is thus satisfied. Using the TBBP to test the Angular stiffness of rotation of bogie,test results show that compared with given value, the error of measurement value using the device is less than 0.041rad,however the error of computed value obtained by the proposed method is within 0.019rad.The effectiveness and real-time performance of the hybrid strategy is further verified.
[1] 苏建, 王金田, 刘玉梅, 等. 一种龙门框架式轨道车辆转向架参数测定试验台:CN103048149A[P]. 2013-04-17. SU Jian, WANG Jintian, LIU Yumei, et al. A gantry frame-type rail vehicle bogie parameter test bench:CN103048149A[P]. 2013-04-17.
[2] 杨廷力, 刘安心, 罗玉峰, 等. 机器人机构拓扑结构设计[M]. 北京:科学出版社, 2012. YANG Tingli, LIU Anxin, LUO Yufeng, et al. Theory and application of robot mechanism topology[M]. Beijing:Science Press, 2012.
[3] 廖明, 刘安心, 沈惠平, 等. 并联机构方位特征集的符号推导方法[J]. 农业机械学报, 2016(3):395-404. LIAO Ming, LIU Anxin, SHEN Huiping, et al. Symbolic derivation of position and orientation characteristics of parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery, 2016(3):395-404.
[4] 李磊. 六自由度并联平台位置正解与控制方法研究[D]. 哈尔滨:哈尔滨工程大学, 2008. LI Lei. Research on forward kinematics and control method of 6-dof parallel platform[D]. Harbin:Harbin Engineering University, 2008.
[5] DAFTARDAR-GEJJI V, JAFARI. H. An iterative method for solving nonlinear functional equations[J]. Math. Anal. Appl., 2006, 316:753-763.
[6] DARVISH M T, BARATI A. A third-order Newton-type method to solve systems of nonlinear equations[J]. Applied Mathematics and Computation, 2007, 187(2):630-635.
[7] 耿明超, 赵铁石, 王唱, 等. 基于拟Newton法的并联机构位置正解[J]. 机械工程学报, 2015, 51(9):28-36. GENG Mingchao, ZHAO Tieshi, WANG Chang, et al. Direct position analysis of parallel mechanism based on Quai-Newton method[J]. Journal of Mechanical Engineering, 2015, 51(9):28-36.
[8] 丁硕, 巫庆辉.基于改进 BP 神经网络的函数逼近性能对比研究[J]. 计算机与现代化, 2012(11):10-13. DING Shuo, WU Qinghui. Performance comparison of function approximation based on improved BP neural net-work[J]. Computer and Modernization, 2012(11):10 -13.
[9] 张宗之, 秦俊奇, 陈海龙, 等. 基于BP神经网络的Stewart平台位姿正解算法研究[J]. 机械传动, 2015(6):54-57. ZHANG Zongzhi, QIN Junqi, CHEN Hailong, et al. Research of the pose forward solution algorithm of Stewart Platform based on BP neural network[J]. Journal of Mechanical Transmission, 2015(6):54-57.
[10] RAHMAN A, GHANBARI A. Application of neural network training in forward kinematics simulation for a novel modular hybrid manipulator with experimental validation[J]. Intelligent Service Robotics, 2016, 9(1):79-91.
[11] 沈惠平, 尹洪波, 王振. 基于拓扑结构分析的求解6-SPS并联机构位置正解的研究[J]. 机械工程学报, 2013, 49(21):70-80. SHEN Huiping, YIN Hongbo, WANG Zhen. Research on forward position solutions for 6-SPS parallel mechanisms based on topology structure analysis[J]. Journal of Mechanical Engineering, 2013, 49(21):70-80.
[12] 裴葆青, 韩先国, 陈五一. 基于传感器的6-DOF并联机构运动学正解[J]. 北京航空航天大学学报, 2005(4):421-424. PEI Baoqing, HAN Xiaoguo, CHEN Wuyi. Solution of direct kinematics of 6-DOF parallel manipulators using extra sensors[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005(4):421-424.
[13] KARDAN I, AKBARZADEH A. An improved hybrid method for forward kinematics analysis of parallel robots[J]. Advanced Robotics, 2015, 29(6):401-411.
[14] 杨廷力, 沈惠平, 刘安心, 等. 机构自由度公式的基本形式、自由度分析及其物理内涵[J]. 机械工程学报, 2015, 51(13):69-80. YANG Tingli, SHEN Huiping, LIU Anxin, et al. Review of the formulas for degrees of freedom in the past ten years[J]. Journal of Mechanical Engineering, 2015, 51(13):69-80.
[15] 尹洪波, 沈惠平, 邓嘉鸣, 等. 球面并联机构的结构降耦及其位置正解求解[J]. 机械科学与技术, 2015, 34(1):51-55. YIN Hongbo, SHEN Huiping, DENG Jiaming, et al. The Reducing in structure coupling and the forward position analysis for the spherical parallel mechanisms[J]. Mechanical Science and Technology for Aerospace Engineering, 2015, 34(1):51-55.
[16] WASEEM M, NOOR M A, NOOR K I. Efficient method for solving a system of nonlinear equations[J]. Applied Mathematics and Computation, 2016, 275:134-146.
[17] GOSSELIN C, SCHREIBER L T. Kinematically redundant spatial parallel mechanisms for Singularity avoidance and large orientational workspace[J]. IEEE Transactions on Robotics, 2016, 32(2):286-300.
[18] YANG C, ZHENG S, JIN J, et al. Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method[J]. Journal of Central South University of Technology, 2010, 17:1264-1270.
[19] SHEN G, TANG Y, ZHAO J, et al. Jacobian free monotonic descent algorithm for forward kinematics of spatial parallel manipulator[J]. Advances in Mechanical Engineering, 2016, 8(4):1687814016645447.
[20] 苏建, 王秀刚, 曹晓宁, 等. 转向架回转特性的测定[J]. 华中科技大学学报, 2013, 41(5):6-10. SU Jian, WANG Xiugang, CAO Xiaoning, et al. Determining Turning Characteristics of Bogie[J]. Huazhong Univ. of Sci. &Tech., 2013, 41(5):6-10.
