Dynamic Model of a Novel Planar Cable Driven Parallel Robot with a Single Cable Loop

Abstract

Cable-Driven Parallel Robots (CDPRs) are a special kind of parallel manipulator that uses cables to control the position and orientation of the mobile platform or end effector. The use of cables instead of rigid links offers some advantages over their conventional rigid counterparts. As cables can only pull but not push, the number of cables (n) required to command the end-effector is always n+1. This configuration is known as fully-constrained, and it is the most extended configuration for CDPRs. Although CDPRs have many advantages, such as their ability to cover large working areas, one of their main problems is that their working area (workspace) is limited in comparison to its frame area (planar case) or frame volume (spatial case), due to the minimum and maximum allowed tensions. Depending on these tension values, the workspace can notoriously decrease. In order to tackle this problem, lots of works focus on solving kinematics or dynamics problems for cable sagging, i.e., they take into account sagging when modelling the robot kinematic and include these poses inside the usable robot workspace. Taking into account phenomena such as this increases the mathematical complexity of the problem, and much more complex techniques are required. On the other hand, the lack of workspace problem can be tackled by adding active or passive elements to the robot design. In this sense, this paper proposes two mechanical modifications: to add passive carriages to the robot frame and to use a single cable loop to command the end-effector position and orientation. This work presents the kinematic, static, and dynamic models of the novel design and shows the gain of workspace for a planar case while taking into account different parameters of the robot.

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“…The end effector's movement results from the cables' tension and length. Due to the use of cables, CDPRs do not work with compressible loads, only tensile ones [28]. The number of cables and the placement of the motors determine the degrees of freedom, stability, and complexity of the robot.…”

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“…The mass of the cables can be ignored, and the elasticity of the cables cannot be ignored. The end effector's mass is large, and there may be substantial speed and acceleration during movements; thus, the mass and inertia of the end effector should not be ignored [39]. The cable's elastic equation for the actuator is as follows:…”

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“…This limited workspace occupancy with regards to the frame size depends on the maximum and minimum tension allowed by the cables. In many practical cases, the workspace can be only between 40-70% of the frame size, which results a strong limitation for industrial application [7]. Extensive research has proposed ingenious solutions to develop methods to extend the workspace of these robots.…”

“…Extensive research has proposed ingenious solutions to develop methods to extend the workspace of these robots. Some authors are trying to increase the workspace by adding passive carriages [8] or using single cable loops [7]. These approaches notoriously increase the feasible workspace but use additional mechanical elements such as large linear guides, which are not always applicable.…”