Kinematic and Dynamic Modelling of Serial Robotic Manipulators Using Dual Number Algebra

Abstract

The kinematic and dynamic modelling of robotic manipulators has, as a specific field of robotics, represented a complex problem. To deal with this, the researchers have based their works on a great variety of mathematical theories (Seiling, 1999). One of these tools is the Dual Algebra, which is a concept originally introduced in 1893 by William Kingdon Clifford (Fisher, 1998; Funda, 1988). A dual number is a compact form that can be used to represent the rigid body motion in the space (Keller, 2000; Pennestri & Stefanelli, 2007), it has therefore, a natural application in the analysis of spatial mechanisms specifically mechanical manipulators (Bandyopadhyay, 2004, 2006; Bayro-Corrochano & Kahler, 2000, 2001). Several works related to dual-number in kinematics, dynamics and synthesis of mechanisms have been developed (Cheng, 1994; Fisher, 1998, 1995, 2003) in (Moon & Kota, 2001) is presented a methodology for combining basic building blocks to generate alternative mechanism concepts. The methodology is based on a mathematical framework for carrying out systematic conceptual design of mechanisms using dual vector algebra. The dual vector representation enables separation of kinematic function from mechanism topology, allowing a decomposition of a desired task into subtask, in order to meet either kinematic function or spatial constraints. (Ying et al, 2004) use dual angles as an alternative approach to quantify general spatial human joint motion. Ying proposes that dual Euler angles method provides a way to combine rotational and translational joint motions in Cartesian Coordinate systems, which can avoid the problems caused by the use of the joint coordinate system due to non-orthogonality. Hence the dual angles method is suitable for analyzing the motion characteristics of the ankle joint. The motion at the ankle joint complex involves rotations about and translations along three axes. In the same field of biomechanics (KiatTeu et al, 2006) present a method that provides a convenient assessment of golf-swing effectiveness. The method can also be applied to other sports to examine segmental rotations. In general, this method facilitates the study of human motion with relative ease. The use of a biomechanical model, in conjunction with dual-number coordinate transformation for motion analysis, was shown to provide accurate and reliable results. In particular, the advantage of using the dual Euler angles based on the dual-