# Kinematic Modeling and Solutions for Cable-Driven Parallel Robots Considering Adaptive Pulley Kinematics

## TL;DR

This paper introduces a new method for modeling and solving the complex movements of cable-driven robots with adaptive pulleys, improving accuracy significantly.

## Contribution

The novel contribution is a hybrid algorithm combining Levenberg–Marquardt and Genetic methods for precise kinematic solutions in adaptive pulley systems.

## Key findings

- A structural analysis of an eight-cable CDPR is conducted.
- A hybrid algorithm achieves high-precision solutions with tracking accuracy better than 1 × 10−7.
- Simulation results validate the effectiveness of the proposed method on various paths.

## Abstract

Although the use of adaptive pulleys enhances the motion characteristics of cable-driven parallel robots (CDPRs), it significantly increases the complexity of the kinematics model. Conventional methods often fail to account for the influence of adaptive pulley motion on cable length variation, making it difficult to establish a precise kinematics model. To deal with the problem, this study presents a kinematic modeling and solution method for CDPRs, which incorporates adaptive pulley kinematics. First, the structural design of the CDPR driven by eight cables is analyzed. Then, the generalized kinematics model and the improved kinematics model with adaptive pulley considerations are established. Furthermore, a hybrid Levenberg–Marquardt and Genetic algorithm is proposed to achieve the efficient and high-precision solution of kinematics equations by combining the rapid global search and precise local optimization. Finally, the proposed method is validated through straight path simulation and elliptical path simulation. The simulation results indicate that the tracking accuracy of the end-effector is better than the 1 × 10−7 level for the proposed method.