The Elastica With End-Load Flip-Over

Abstract

A high flexure manipulator arm is modeled as an elastic cantilever beam with a tip payload and an eccentric tip follower load that drives the arm. Shapes of the resulting elastic curves for finite deformations (the elastica) are calculated in terms of nondimensional system parameters. For critical combinations of these parameters, a small increment in the driving follower load causes an abrupt change in the shape of the elastica. The abrupt change in tip angle is typically of the order of π radians. These results are applicable to the design of high flexure robotic manipulators.