This paper presents a new formulation as well as numerical solution for the problem of finding a point-to-point trajectory with maximum load carrying capacities for flexible manipulators. For rigid manipulators, the major limiting factor in determining the maximum allowable load (mass and mass moment of inertia) is the joint actuator capacity, while the flexibility exhibited by light weight robots or by robots operating at a higher speed dictates the need for an additional constraint to be imposed for situations where precision tracking is required, that is, the allowable deformation at the end effector. The Lagrangian assumed mode method was used to model the manipulator and load dynamics, including both joint and deflection motions. An Iterative Linear Programming (ILP) method is then used to determine the maximum allowable load of elastic robot subject to both constraints, while a general computational procedure for the multiple-link case given arbitrary trajectories is presented in detail. Symbolic derivation and simulation by using a PC-based symbolic language MATHEMATICA® was carried out for a two-link planer robot and the results further confirm the necessity of the dual constraints.

Rough joint flexibility is the dominant source of compliance in today's commercial robots in future robots containing light weight flexible arms link flexibility may become most important. Hence this paper stresses link flexibility rather than joint flexibility.