Denavit-Hartenberg Parameters of Euler-Angle-Joints for Order (N) Recursive Forward Dynamics

TLDR: In this paper, the authors introduce the concept of Euler-angle-joints (EAJs) which are nothing but three revolute joints so connected by imaginary links with zero length to represent particular Euler angles.

Abstract: Euler angles are generally used for representing rigid body rotation in three dimensions. In this paper we introduce a concept of Euler-angle-joints (EAJs) which are nothing but three revolute joints so connected by imaginary links with zero length to represent particular Euler angle set. These EAJs can be represented using the well-known Denavit-Hartenberg (DH) parameters. The proposed EAJs are useful in representing a spherical joint present in any multibody system. One can then derive a corresponding decoupled natural orthogonal complement (DeNOC) matrices used in dynamic formulation to obtain the analytical expressions of the generalized inertia matrix elements in scalar form. These expressions are used to develop an O(n) — n being the number of degree-of-freedom of a serial chain — recursive forward dynamics algorithm. The methodology suggested is illustrated with a numerical example.Copyright © 2009 by ASME