# Dynamics of serial kinematic chains with large number of degrees-of-freedom

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## Abstract

This paper investigates the dynamic behaviour of serial chains with degrees-of-freedom (DOF) as large as 100,000. A recursive solver called Recursive Dynamic Simulator (ReDySim), based on the Newton–Euler formulation and the Decoupled Natural Orthogonal Complement (DeNOC) matrices, was used to simulate the dynamics of these systems. Planar, as well as spatial motions of chains with moderate- (DOF≤1,000), large- (1,000<DOF≤10,000), and huge- (DOF>10,000) DOF were simulated. The results were validated by several means, such as comparisons with reported results wherever available, results obtained from commercial software, energy checks, etc. The study shows that ReDySim is capable of analysing serial chains of huge-DOF with acceptable numerical accuracy. The scheme is found to be numerically stable as well as computationally efficient, owing to the linear-time computation of the joint accelerations. Numerical studies were conducted to establish the theoretical basis for better performance of the proposed ReDySim solver. With the demonstrated capabilities of ReDySim, it may be found suitable for a large number of applications involving serial systems with huge-DOF.

## Keywords

Dynamics Chains Decomposition Large degrees-of-freedom## Notes

### Acknowledgements

The authors acknowledge the Naren Gupta Chair Professor fund of the last author at IIT Delhi, which was used to support the second author to conduct this research. Anonymous reviewers are also thanked for their constructive comments.

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