6自由度船舶摇摆平台无奇异工作空间的分析

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For the 6 degree of freedom parallel mechanism of ship swaying platform,the singular phenomenon is inevitable during kinematic and dynamic analyses.Mechanism in singular state can change the original design of motion trajectory,and greatly affect the control performance.Based on the method of RPY describe rotation matrix,the swaying platform kinematic singularity problem was investigated to obtain a Jacobian matrix.The determinants were solved to obtain the singularity which was directly relative to analytical expression with six position and attitude variables.By Mathematica software,the swaying platform position singularity and posture singularity were simulated to draw the locus of singular position and singular attitude.The singular phenomenon during the control trajectory design was effectively avoided.By Matlab software,the singular value constraint was introduced to solve mechanism work space and program search algorithm.The mechanism in a fixed posture with singularity-free position work space was achieved to provide theoretical basis for general parallel mechanism control.6自由度船舶摇摆平台的并联机构,在运动学、动力学分析中,奇异现象不可避免,机构处于奇异状态,会改变原来设计的运动轨迹,极大影响机构控制性能.采用了RPY方法描述旋转矩阵,研究该摇摆平台的运动学正解奇异性问题,得到一种雅可比矩阵.对其求解行列式得到奇异性直接关于6个位姿变量的解析表达式.应用Mathematica软件分别对摇摆平台位置奇异和姿态奇异进行了计算仿真,并绘制了奇异位置和奇异姿态的轨迹图,有效避免在控制轨迹设计时出现的奇异现象.最后在求解机构工作空间中,首次引入奇异值约束条件,利用Matlab软件,编写搜索算法,得到机构在固定姿态下的无奇异位置工作空间,为一般并联机构的控制提供理论基础.