Abstract
This paper focuses on the kinematics, kinetostatics and design optimization of a 2-DOF cable-driven flexible joint module. Based on the motion characteristics of the 2-DOF joint module, the concept of instantaneous screw axis in conjunction with the Product-Of-Exponentials (POE) formula is proposed to formulate its kinematic model. However, as the instantaneous screw axis is unfixed, the Lie group method is employed to derive the instantaneous kinematic model of the joint module. In order to generate the feasible workspace subject to positive tension constraint, the kinetostatics of the joint module is addressed, where the stiffness resulting from both the driving cables and the flexible backbone are considered. A numerical orientation workspace evaluation method is proposed based on an equi-volumetric partition in its parametric space and the volume-element associated integral factor. A global singular value (GSV) index, which considers the minimum singular value of the stiffness matrix of joint module over the achievable workspace, is employed to optimize the geometric size of joint module. The simulation results demonstrate the effectiveness of the proposed GSV optimization algorithm.
Highlights
The flexible Snake‐Like Robot Arm (SLRA) with hyper‐ redundant Degrees Of Freedom (DOF) is especially suitable for the industrial applications requiring high manoeuvrability over complex and confined spaces such as on‐wing inspection and repair of airplanes [1] and search and rescue in collapsed buildings [2]
In order to improve the performance of the Cable‐ Driven Snake‐like Robot Arm (CDSLRA), design optimization of the 2‐DOF cable‐driven joint module with a flexible backbone becomes a very critical issue, which, has not been well‐ addressed due to the lack of effective kinematics, kinetostatics and workspace analysis models
This means that a larger ratio r/L can lead to a larger global singular value (GSV) index, i.e., better stiffness performance
Summary
The flexible Snake‐Like Robot Arm (SLRA) with hyper‐ redundant Degrees Of Freedom (DOF) is especially suitable for the industrial applications requiring high manoeuvrability over complex and confined spaces such as on‐wing inspection and repair of airplanes [1] and search and rescue in collapsed buildings [2]. To represent the 2‐DOF bending motions using Euler angles, three sequential rotations (Rz( )Ry( )Rz(‐ )) are needed in order to remove the twisting motion about the backbone, only two Euler angles ( and ) are used To avoid such a problem, the instantaneous screw axis concept is proposed in this paper such that the 2‐DOF bending motion of the joint module can be clearly described by one rotation about an instantaneous screw axis with its directional component parallel to the x‐y plane of the base frame. With such a geometrically meaningful concept, the POE formula [5] can be employed to formulate the kinematic models of the 2‐DOF joint module, making the analysis significantly simplified. Based on the manipulator Jacobian of the 2‐ DOF joint module, an instantaneous kinematics model is derived for the joint module, which will be used in the following analysis
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