Evolution of the DeNOC-based dynamic modelling for multibody systems

Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples.

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

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.