This paper investigates the minimum cable tension distributions in the workspace for cable-based parallel robots to find out more information on the stability. First, the kinematic model of a cable-based parallel robot is derived based on the wrench matrix. Then, a noniterative polynomial-based optimization algorithm with the proper optimal objective function is presented based on the convex optimization theory, in which the minimum cable tension at any pose is determined. Additionally, three performance indices are proposed to show the distributions of the minimum cable tensions in a specified region of the workspace. An important thing is that the three performance indices can be used to evaluate the stability of the cable-based parallel robots. Furthermore, a new workspace, the Specified Minimum Cable Tension Workspace (SMCTW), is introduced, within which all the minimum tensions exceed a specified value, therefore meeting the specified stability requirement. Finally, a camera robot parallel driven by four cables for aerial panoramic photographing is selected to illustrate the distributions of the minimum cable tensions in the workspace and the relationship between the three performance indices and the stability.
Cable-based parallel robots whose end-effectors are manipulated by motors that can extend or retract the cables are a type of robotic manipulator that has recently attracted interest for large workspace manipulation tasks. They show several promising advantages over their rigid-link counterparts, such as simple light-weight mechanical structure, low moment inertia, large reachable workspace, and high-speed motion. Thus, a wide variety of cable-based robots have been used in medical rehabilitation, material transportation, wind tunnel experiment, astronomical observation, and other fields [
This paper addresses the minimum cable tension distributions in the workspace for cable-based parallel robots. First of all, the determination of the cable tensions of completely restrained parallel robots is presented. This problem is treated as a noniterative polynomial-based optimization algorithm with an optimal objective function based on the convex optimization theory. Moreover, the minimum cable tension at any pose is determined and SMCTW is introduced based on the concepts of minimum cable tension and workspace. Subsequently, three performance indices are developed to explain the distributions of the minimum cable tensions in the workspace. Additionally, the results and discussion are given in Section
A cable-based parallel robot is represented schematically in Figure
Kinematic modeling of a cable-driven parallel mechanism.
Referring to Figure
When tensions are maintained in all cables, cable
Thus using Newton method from (
From (
The feasible solution
Form (
The minimum cable tension
In order to get any more information about the stability of a cable-based parallel robot, three performance indices are proposed to show the distributions of the minimum cable tensions in the some regions of the workspace based on the minimum cable tensions. The three performance indices are
Schematic diagram of the three performance indices.
The three performance indices can be expressed as
Referring to Figure
Furthermore, SMCTW is composed of the positions that have specified minimum cable tensions. According to [
The workflow of SMCTW generation algorithm can be summarized as follows. Input the real-time platform position Calculate the structure matrix Obtain the null space matrix Find the optimum value Calculate the minimum cable tension Judge whether Judge if
An example is now presented in order to illustrate the distributions of the minimum cable tensions in the workspace and the relationship between the three performance indices and the stability. A spatial three-degree-of-freedom cable-based parallel robot with four cables that is called camera robot is used for simulation and analysis [
The camera robot structure is displayed in Figure
Schematic diagram of a camera robot.
As shown in Figure
The minimum cable tensions on the different vertical and horizontal planes are depicted in Figure
The minimum cable tensions on two different vertical planes are depicted in Figure
The minimum cable tensions at different elevations are depicted in Figure
The three performance indices above are computed using (
The three force performance indices in the workspace.
From the simulation results and analysis above it can be concluded that the camera robot can move stably and reliably at the positions that contain bigger performance indices just due to the relatively large minimum cable tensions and uniformity of the tensions.
The minimum cable tension distributions for completely restrained cable-based parallel robots are discussed using the three performance indices based on the cable tension determining. Solutions to the problems of minimum cable tension distributions are presented to a typical camera robot. Simulation results of the three performance indices show that as the three performance indices increase, so do the minimum cable tensions and the constraints of the weakest direction, therefore improving the stability of the movement. In the whole workspace, the positions in the center and on top of the workspace possess bigger minimum cable tensions than others, leading to having better stability. It is important to notice that the positions within the surface formed by a specified
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the financial support of National Science Foundation of China under Grant nos. 51175397 and 51105290.