Parámetros De Denavit Hartenberg Modificados Por Kahlil

A NEW GEOMETRIC NOTATION F R OPEN AND CLOSED-LOOP O ROBOTS

W. KHALIL - J.F.

KLEINFINGER

Laboratoired'AutomatiquedeNantes UA C.N.R.S. 04/823 1 r u e d e l a N o & 44072 NANTES CEDEX - FRANCE E.N.S.M. ABSTRACT T h i s p a p e r p r e s e n t s a new g e o m e t r i c n o t a t i o n f o r t h e d e s c r i p t i o no ft h ek i n e m a t i co fo p e n - l o o p .t r e ea n dclosed-loopstructurerobots. The mechod i s d e r i v e d (D-H) from t h e well-known DenavitandHartenberg notation,which i s powerfulfor serial r o b o t s b u t t r e e andclosedleadstoambiguitiesinthecaseof loop s t r u c t u r e r o b o t s . The g i v e n method h a s a l l the advantagesof D-H n o t a t i o n i n t h e c a s e o f o p e n - l o o p robots. 1 INTRODUCTION frame R . i s a s s i g n e d f i xe d w i t h r e s p e c t t o l i n k The a x i so fj o i n t .
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t o L i - l and Z . ( F i g . 1-a)
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is e q u a l t o

= R o t ( 2 , e . )T r a n s ( 2, r . )T r a n s ( X , d i )R o t ( X , a i )

Many methods are a v a i l a b l e f o r t h e d e s c r i p t i o n o f w i t h open-chain mechanism [ I ] . thegeometryofrobots The most common use i s t h e e l e g a n t D-H method [ 2 ] . TheD-H method i s d e a l i n g w i t h l i n k s w i t h o n l y two j o i n t s . The d e f i n i t i o n of a j o i n t w i t h r e s p e c t t o the preceeding one i s c a r r i e d o u t b y means of 4 parameters. The u s e o f D-H n o t a t i o n i n r o b o t i c s h a s (geomef a c i l i t e d g r e a t l y a l l themodelingproblems t r i c kinematics,anddynamics) [ 3 ] . The D-H n o t a t i on , as it is, however, i s s t i l l powerfulanduseful hamperedby c e r t a i n d i f f i c u l t i e s . I n f a c t , the a p p l i D-H n o t a t i o n t o r o b o t s w i t h l i n k s cation of the having more t h a n two j o i n t s i s d i f f i c u l t a n d l e a d s to ambiguities [ 4 ] . ShethandUicker (S-U) [ 4 ] h a sd e v e l o p e da n o t h e r n o t a t i o n which d e s c r i b es e a c h l i n k by 7 parameters. The S-U methodcanbeused t o d e s c r i b e a n y mechanism, b u t owing t o i t s complexity it h a s b e e n a p p l i e d o n i y [5]. f o rt h ec l o s e d - l o o pr o b o t s In this paper we propose a new g e o m e t r i c n o t a t i o n which can be used for both the closed and the openD-H notalooprobots. It has a l l theadvantagesof t i o n when u s ed f o r o p e n - c h a i n r o b o t s , a n d c a n e a s i l y robots. I n t h e case of b eu s e df o rt h ec l o s e d - l o o p l i n k s w i t h 2 j o i n t s , 4 parameters are needed t o d e s c r i b e a j o i n t w i t h r e s p e c t t o the p r e c e e d i n g o n e , while 2 a d d i t i o n a l p a r a m e t e r s may be needed i n t h e case o f l i n k s w i t h more t h a n t w oj o i n t s . Inthefollowing two s e c t i o n s we w i l l p r e s e n t the D-H and the S-H n o t a t i o n s . The p r o p o s e d n o t a t i o n w i l l be presented in section 4. Two examples w i l l be 5 to illustrate the given notation. giveninsection

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1 1

is r o t a t i o n a l...