Orthogonal second-order Cartesian tensors are used to formulated the Newton-Euler dynamic equations for a robot manipulator. Based on this formulation, an efficient recursive procedure is developed to evaluate the joint torques. The procedure is applicable to all rigid-link manipulators with open-chain kinematic structures with revolute and/or prismatic joints. For simplicity of presentation, only manipulators with (kinematically more complex) revolute joints are considered. An efficient implementation of the proposed method shows that the joint torques for a six-degree-of-freedom manipulator with revolute joint, can be computed in approximately 500 multiplications and 420 additions. For manipulators with 0 degrees or 90 degrees twist angles, the required computations are reduced to 380 multiplications and 315 additions.>

The authors use orthogonal second-order Cartesian tensors to formulate the Newton-Euler dynamic equations for a robot manipulator. Based on this formulation, they develop two efficient recursive algorithms for computing the joint actuator torques/forces. The proposed algorithms are applicable to all rigid-link manipulators with open-chain kinematic structures with revolute and/or prismatic joints. An efficient implementation of one of the proposed algorithms shows that the joint torques/forces for a six-degrees-of-freedom manipulator with revolute joints, can be computed in approximately 489 multiplications and 420 additions. For manipulators with zero or 90 degrees twist angles, the required computations are reduced to 388 multiplications and 370 additions. For manipulators with even simpler geometric structures, these arithmetic operations can be further reduced to 277 multiplications and 255 additions.>

A computational method for recursive evaluation of linearized dynamic robot models about a nominal trajectory is presented. The forward method evaluates the "sensitivity matrices" necessary to calculate the "forward" dynamics of the linearized model. The method has made efficient by using the fact that the derivatives of trigonometric functions need not be computed explicitly and that the partial derivatives of the homogeneous transformation matrices, may be obtained merely by row and column manipulations. The proposed scheme is general in nature and can be applied efficiently to manipulators having revolute and prismatic joints.