Systematic methods for efficient modeling and dynamics computation are developed, using the Lagrangian assumed modes method. The methods greatly reduce the number of mathematical operations (i.e. multiplications and additions) required for the modeling and dynamics computation of flexible manipulators. The link deflection is described by a truncated modal expansion. The operations of 3*3 matrices and/or 3*1 vectors only exist in the methods. All the dynamics computations are performed in the link coordinate systems, in which the kinematics information is computed with the forward recursion from the base to the hand tip and the dynamics information is computed with the return recursion. As compared with other existing methods, the methods proposed here are computationally more simple, systematic, and efficient. Simulation results for a single-link flexible robot manipulator are presented to verify the methods and the algorithms proposed.>

A method for linearizing dynamic models for robot manipulators along a nominal trajectory for robot manipulators is developed from the straightforward Lagrangian formulation. The method is very simple and systematic. It can be applied both to the computation of the feedforward control law (i.e. the joint generalized forces/torques) along the desired nominal trajectory and to the design of the feedback controller that reduces or eliminates any deviations from the desired nominal trajectory. The salient advantage of using this method is that the amount of computation required for deriving the complete linearized dynamic model for a manipulator is so small that it makes the real-time computation on a mini- or microcomputer possible. The computation for a general manipulator with six degrees of freedom requires at most 2000 multiplications and 1700 additions. For most industrial manipulators with six degrees of freedom, it requires at most 1400 multiplications and 1300 additions.>

An efficient method for linearizing dynamic models about a nominal trajectory is developed from the straightforward Lagrangian formulation. The method is very simple and systematic. It can be applied to compute the feedforward control law (i.e. the generalized forces or torques) about the desired nominal trajectory and to design the feedback controller that reduces or eliminates any deviations from the desired nominal trajectory. The salient advantage of the method is that the number of computations for deriving the complete linearized dynamic models for a manipulator is so few as to allow real-time computation on a mini- or microcomputer. The total number of computations to derive the complete linearized dynamic models (including the computation of the joint generalized forces or torques) about the nominal trajectory for a manipulator with six degrees of freedom is at most 2600 multiplications and 2711 additions. Computationally, this method is the fastest of all existing methods.>

A novel method of determining the dynamics for robot manipulators has been developed from Lagrangian mechanics. This method can solve the problem in which the number of computations is numerous when the Lagrange-Euler method is used for deriving a set of closed and explicit-form differential or state equations for robot manipulators. The method can be applied to the design of control systems, the dynamic simulation, and the computation of generalized forces or torques of robot manipulators. The number of computations of using this method is small enough to allow real-time computation on a minicomputer or microcomputer. The whole computational process for deriving the complete dynamic equations of a robot manipulator with n degrees of freedom requires at most (3n/sup 3//2+14n/sup 2/+79n/2-4) multiplications and (7n/sup 3//6+10n/sup 2/+115n/3-10) additions.>

In this paper, a new method for the dynamic analysis of robot is developed from the Lagrange-Euler equation. This new method can solve those problems which needs too much amount of calculation when dynamic analysis of robot is performed with Lagrange-Euler method. When it is used in the dynamic analysis of open chain robot with 6 degree-of-freedom, the whole calculating process, including the calculation of the homogeneous transformation matrices needs only 1,436 multiplications and 1,092 additions.