Automatic algebraic computation of basic kinematic equations of tree structure robot arms: application to human arms.

Tree structure robot arms have been very little studied due to the complexity of their topological structure compared with those of the simple chain type. This paper presents a symbolic computation of the basic kinematic equations of these tree structure robot arms. This leads to the calculation of the homogeneous transformation matrices (HTMs) of the tree branches. These computations are arranged to need the smallest possible number of arithmetic operations. A computer program MGLAT is developed in Pascal to generate such equations in symbolic form. The human arm which consists of the forearm, a wrist and fingers is a very good example of such a structure. A simplified model of 25 degrees of mobility of such an arm is presented. Its basic kinematic equations need 358 multiplications, 214 additions and 252 equations. These equations are useful for improving the existing designs of the artificial arms for handicapped persons and for designing new robot hands for delicate tasks.