A PLANAR ROBOT DESIGN AND CONSTRUCTION WITH MAPLE

Abstract

Maple is used to do numerical computation, plot graphs and do exact symbolic manipulations and word processing. In this study we demonstrate how Maple can be used for the simulation of a planar robot. This offers the possibility to become familiar of mathematical modelling. The mechanism under consideration is a so-called F-mechanisms (Can & Stachel, 2014), i.e., a planar parallel 3-RRR robot with three synchronously driven cranks. It turns out that at this example it is not possible to find the poses of the moving triangle exactly by graphical methods with traditional instruments only. Hence, numerical methods are essential for the analysis of motions which can be performed by a planar robot

Keywords

• Maple, scientific computing, mathematical modelling, planar mechanism, planar parallel 3-RRR-robot

References

1. Can, E. & Stachel H. (2014). A planar parallel 3-RRR robot with synchronously driven cranks. Mechanism and Machine Theory 79 (pp. 29-45).
2. Can, E. (2012). Analyse and Synthese eines schnelllaufenden ebenen Mechanismus mit modifizierbaren Zwangläufen. PhD Thesis, Vienna University of Technology.
3. Can, E. (2015). Über die Verwendung von MAPLE für die Simulation von Mechanismen. Teaching Mathematics and Computer Sciences 13/1 (pp. 21-39).
4. Ahamed, S. Simulation of a 3-DOF 3-RRR Planar Parallel Robot, www.parallemic.org/Java/3RRR.html
5. Gander, W. & Hrebicek, J. (2004). Solving Problems in Scientific Computing Using Maple and Matlab. Heidelberg Springer, Berlin.
6. Staicu, S. (2008). Kinematics of the 3-RRR planar parallel robot. U.P.B. Sci. Bull. Ser. D. 70/2 (pp. 3–14).
7. Wunderlich, W. (1970). Ebene Kinematik. BI–Hochschultaschenbücher, Bd. 447. Bibliographisches Institut, Mannheim.