exposes nonideal behavior such as finite op-amp slew and current end effector is oriented quickly, continuously, and isotropically in drive, putting limitations on the rates at which an array can be all directions. The performance of the popular three-consecutive-roaddressed by a real interface. In time these further issues will be tational-joints wrist, which possesses singularities within its analyzed, and the tradeoffs arising there will be better understood. workspace [l], 121, is less than optimum.

This paper presents t h e design concept of a new spherical stepper robotic w r i s t motor capable o f t h r e e DOF spherical motor and t h a t of t h e conventional s t e p p e r motor. The authors seek t o e s t a b l i s h a t h e o r e t i c b a s i s f o r design, prototype development and performance prediction. In p a r t i c u l a r , an a n a l y s i s of torque prediction i s discussed along with t h e presentation of kinematic and dynamic r e l a t i o n s h i p . A laboratory prototype hybrid d i g i t a l /analog control c i r c u i t r y has been developed t o demonstrate proof of concept f e a s i b i l i t y and t o a s s i s t i n achieving an optimum design. 1. INTRODUCTION Recent developments i n r o b o t i c s , d a t a driven manufacturing and high p r e c i s i o n assembly have provided t h e motivation f o r t h e resurfacing of unusual designs of electromechanical transducers. A f l u r r y of research a c t i v i t y i s c u r r e n t l y underway i n d i r e c t d r i v e s involving DC, stepping, and brushless electro-mechanical a c t u a t o r s t o improve performance by eliminating t h e problems inherent i n t h e gear systems such a s backlash, f r i c t i o n due t o meshing, and mechanical compliance. These devices a r e normally employed t o accomplish a s i n g l e degree of motion manipulation a t each j o i n t . An a l t e r n a t i v e design based on t h e concept o f a spherical stepper w r i s t motor presents some a t t r a c t i v e p o s s i b i l i t i e s by combining p i t c h , r o l l , and yaw motion i n a s i n g l e j o i n t . In addition t o the compact design, t h e spherical w r i s t stepper motor r e s u l t s i n r e l a t i v e l y simple j o i n t kinematics and has no s i n g u l a r i t i e s in t h e middle of t h e workspace except a t t h e boundaries.

The research is to establish the theoretical basis for the design, dynamic modeling and control of a spherical wrist motor which presents some attractive possibilities by combining pitch, roll, and yaw motion in a single joint. The spherical wrist motor has potential applications where the demand on workspace is low but for high-speed precision isotropic manipulation of end-effector orientation, is required continuously in all directions. In this paper, both the finite-element method and the permeance-based model are used for the design and control of the spherical stepper motor. The results of the finite-element method provide the necessary knowledge on the magnetic flux patterns, which are essential for design optimization and dynamic modeling for spherical motor control.