The Reach Envelope of a 9 Degree-of-Freedom Model of the Upper Extremity
IOWA UNIV IOWA CITY CENTER FOR COMPUTER AIDED DESIGN
Pagination or Media Count:
This paper presents a rigorous mathematical formulation for modeling the upper extremity that is capable of considering a relatively large number of degrees of freedom, thus yielding a realistic model and associated envelope. Kinematic models are used to determine the reach envelope in closed-form and to better understand human motion. Joint ranges of motion are taken into account by transforming unilateral inequality constraints into equalities that are included in the formulation. Methods from geometry are implemented to analyze the motion and delineate barriers within the workspace. It is observed that these barriers are indeed surfaces where the limb has one or more joints at their limits, but also where the hands motion has encountered a kinematic singular configuration. Such a configuration is mathematically defined and is physically associated with two links being parallel at an instant in time or where two joints have their axes parallel e.g., a fully extended arm yields a singular configuration. Barriers to motion can now be characterized in terms of different human performance measures, thus leading to a better understanding of the path trajectories assumed by humans as they execute tasks.
- Anatomy and Physiology
- Statistics and Probability