# An Enhanced Dynamic Model of a Spatial Parallel Mechanism Receiving Direct Constraints from the Base at Two Point-Contact Higher Kinematic Pairs

## TL;DR

This paper introduces a biologically inspired parallel mechanism for 3D chewing simulation, with a focus on dynamic modeling and friction effects.

## Contribution

The paper proposes an inverse dynamic model using Euler parameters for a parallel mechanism with direct constraints and friction effects.

## Key findings

- The model using Euler parameters consumes only 23% of the time compared to the model using Euler angles.
- Friction effects significantly increase the model's nonlinearity.
- Direct constraints from the base raise modeling complexity and computational cost.

## Abstract

In this paper, a biologically congruent parallel mechanism (PM) inspired by the masticatory system of human beings has been proposed to recreate complete chewing behaviours in three-dimensional space. The mechanism is featured by direct constraints from the base (DCFB) to its end effector at two higher kinematic pairs (HKPs), which greatly raise its topological complexity. Meanwhile, friction effects occur at HKPs and actuators, causing wear and then reducing motion accuracy. Regarding these, an inverse dynamic model that can raise the computational efficiency and the modelling fidelity is proposed, being prepared to be applied to realise accurate real-time motion and/or force control. In it, Euler parameters are employed to express the motions of the constrained end effector, and Newton–Euler’s law is applied, which can conveniently incorporate friction effects at both HKPs and actuators into the dynamic model. Numerical results show that the time consumption of the model using Euler parameters is only approximately 23% of that of the model using Euler angles, and friction effects significantly increase the model’s nonlinearity. Further, from the comparison between the models of the target PM and its counterpart free of DCFB, these constraints sharply raise the modelling complexity in terms of the transformation between Euler parameters and Euler angles in the end effector and the computational cost of inverse dynamics.