Title :
The closure condition of the double banana and its application to robot position analysis
Author :
Rojas, Nicolas ; Thomas, F.
Author_Institution :
Inst. de Robot. i Inf. Ind., UPC, Barcelona, Spain
Abstract :
A double banana is defined as the bar-and-joint assembly of two bipyramids joined by their apexes. Clearly, the bar lengths of this kind of assembly are not independent as we cannot assign arbitrary values to them. This dependency can be algebraically expressed as a closure condition fully expressed in terms of bar lengths. This paper is devoted to its derivation and to show how its use simplifies the position analysis of many well-known serial and parallel robots thus providing a unifying treatment to apparently disparate problems. This approach permits deriving the univariate polynomials, needed for the closed-form solution of these position analysis problems, without relying on trigonometric substitutions or difficult variable eliminations.
Keywords :
computational geometry; manipulator kinematics; polynomials; position control; bar lengths; bar-and-joint assembly; bipyramid assembly; closed-form solution; double banana closure condition; parallel robots; robot position analysis; serial robots; trigonometric substitutions; univariate polynomials; variable eliminations; Assembly; Joining processes; Joints; Kinematics; Polynomials; Robots;
Conference_Titel :
Robotics and Automation (ICRA), 2013 IEEE International Conference on
Conference_Location :
Karlsruhe
Print_ISBN :
978-1-4673-5641-1
DOI :
10.1109/ICRA.2013.6631237