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INVERSE KINEMATICS PROBLEM FORMULATION
SOLUTIONS FOR SINGULAR CONFIGURATIONS
3 other sections not shown
4th-order function angle backward procedure bring the problem Chapter defined degrees of freedom eight second-order equations exact analytical solutions FORWARD1 function of 62 gripper orientation initial configuration inverse kinematics problems iteration Jacobian matrix joint axes joint constraints joint variables Kakazu kinematics equations Link parameters main algorithm matrices Milacron T3-776 robot Newton-Raphson method numerical algorithm numerical method obtained by solving orientation error orientation singularities pattern plugged position and orientation position or orientation prismatic axis problem into stage problem of stage REFERENCE DIRECTION represented requires solving revolute axis revolute joint robot right hand side robot configuration second-order function second-order terms secondary algorithm seven revolute joint shown simplify the kinematics singular directions six revolute joints solve 65 solved by solving solving two fourth-order special geometry special robot geometries stage 2 problem step target location Target orientation target position three fourth-order equations three parallel revolute three variables Tsai and Morgan unit vector velocity