Maximum allowable load of flexible manipulators for given dynamic trajectory

Abstract

This paper presents the formulation and numerical solution of the dynamic load carrying capacity (DLCC) problem of flexible manipulators. For manipulators under the rigid body assumption, the major limiting factor in determining the maximum allowable load (load mass and load moment of inertia) for a prescribed dynamic trajectory (positions, velocities and accelerations) is the joint actuator capacity. But for a flexible robot, an additional constraint on allowable deformation at the end effector must be imposed because either lighter-weight links or operating at a higher speed could cause unacceptable fluctuations when moving along a trajectory. A Lagrangian assumed mode method was used to model the manipulator and load dynamics, including both joint and deflection motions. The deflection equations are then coupled with robot kinematics to solve for the generalized coordinates. A strategy to determine the DLCC subject to both constraints mentioned above is formulated where the end effector deflection is specified in terms of a series of spherical bounds with a radius equal to the allowable deformation. A general computational procedure for the multiple-link case given arbitrary trajectories is described in detail. Symbolic derivation and simulation by using a PC-based symbolic language MATHEMATICA® was carried out for a two-link planer robot. The results confirmed the necessity of the dual constraints and showed that which constraint is more critical for a given robot and trajectory depends on the required accuracy.