Mininum-time along the path for a mechanical arm

I HTROWCT I ON The t r a v e l i n g p a t h of a mechanical manipulator i s canposed o f s t r a i g h t l i n e s e g m n t s i n C a r t e s i a n coordinates connected by smooth arcs. The manipu-l a t o r r e s t s a t i t s i n i t i a l p o s i t i o n b e f o r e it moves, and s t o p s a t i t s f i n a l p o s i t i o n. The j o i n t s o f t h e manipulator are driven by e l e c t r i c a l motors and c o n t r o l l e d by servo systems which are designed for the worst case. In actual operation, the manipula-tor t h u s p e r f o r m below i t s c a p a b i l i t y. I n a d d i-tion, conventional controls are designeA +such a way that the manipulator stops at the end, ne seg-It i s seen t h a t t h e e l i m i n a t i o n o f t h e s t o p a t t h e end o f each l i n e segnent and the use o f t h e maximum v e l o c i t y under physical constraints w i l l allow the manipulator t o move more r a p i d l y and hence the travel ing t i m e i s reduced. on the arc of the actual path from the corner of two adjacent straight line segments must be kept s m a l l enough so that the actual path does not s i g n i f i c a n t l y d e v i a t e from the planned path. Otherwise i t may have a r i s k o f r u n n i n g i n t o obstacles. These …