Abstract
Morse theory plays a central role when we study the configuration space of various mechanical linkages. As an important linkage, we consider the planar robot arm. It is known that the distance function on its configuration space is a Morse function. On the other hand, for a fixed angle θ, we consider the spatial robot arm whose adjacent bond angles are θ. In chemistry, such an arm is used as a model for protein backbones and has been studied extensively. We consider the distance function on its configuration space. The purpose of this chapter is threefold: First, we study whether the distance function is a Morse function. Second, we determine the minimum and maximum values of the function. Consider the case that the arm consists of four bars. Then our third purpose is to study how the distance function is different from the usual Morse function on the torus.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
