Generic one-parameter bifurcations in the motion of a simple robot

Abstract

In the car manufacturing industry, painting and polishing work is mostly done by robots because these tasks are quite hazardous to the health of human workers, and also because they do not require a very sophisticated robot. In general the industrial product (car) passes by the robot with constant speed, and the endpoint of the robot where the painting device, usually a spray pistol, is mounted, performs a prescribed time periodic motion. For such a painting process stability problems can become important if parameters are varied. Two cases should be mentioned as examples. Firstly, if the speed of the assembly line is increased, the endpoint of the robot must also move faster and hence a loss of stability of the basic periodic motion can occur for fixed parameters of the controller. Secondly, a change of the spray pistol to one with different mass again is a variation of a parameter which could lead to an instability.