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The kinematics analysis method of a novel 3-DOF wind tunnel mechanism based on cable-driven parallel mechanism is provided. Rodrigues' parameters are applied to express the transformation matrix of the wire-driven mechanism in the paper. The analytical forward kinematics model is described as three quadratic equations using three Rodridgues' parameters based on the fundamental theory of parallel mechanism. Elimination method is used to remove two of the variables, so that an eighth-order polynomial with one variable is derived. From the equation, the eight sets of Rodridgues' parameters and corresponding Euler angles for the forward kinematical problem can be obtained. In the end, numerical example of both forward and inverse kinematics is included to demonstrate the presented forward-kinematics solution method. The numerical results show that the method for the position analysis of this mechanism is effective.

Parallel manipulators have separate serial kinematic chains that are linked to the ground and the moving platform at the same time. They have some potential advantages over serial robot manipulators such as accuracy, greater load capacity, higher velocities, and accelerations. Parallel manipulators have been developed for applications in many fields [

In the past few decades, parallel manipulators using cable transmission have been enthusiastically studied in a number of areas. In a cable suspended parallel robot, the moving platform is suspended and manipulated by the attached cables that are connected to the base; for example cable-suspended robots are Robocrane [

In recent years, many researchers paid great attention to the use of cable-driven mechanism in wind tunnel test due to its fewer interference on the streamline flow. Some successful achievements have been made in the Suspension ACtive pour Soufflerie (

However, recent works about cable-driven wind tunnel mechanism (CDWTM) have focused on the design of 6 degree-of-freedom (DOF); further research is still under way to meet practical application. This article puts forward a new 3-DOF wind tunnel equipment based on cable-driven parallel mechanism, which can provide 3-DOF pure rotation for the scale model in wind tunnel. Because position analysis is one of the key complicated and important problems for the cable-driven parallel mechanism, the forward and inverse kinematics of the aforementioned mechanism is the main concern of the paper. In general, a numerical iterative scheme, such as Newton-Raphson method, can be applied to this problem. But such method not only demands an initial estimate that should be fairly close to the solution of the current configuration but also cannot guarantee the convergence to the actual solution. As is well known there are many methods that can be used to express transformation matrix in the closed-form solution for position analysis; in [

The reminder of the paper is the following. Section

Figure

Functional schematic of a 3-DOF CDWTM.

Choose Rodridgues vector

Here

Furthermore, the inverse of

From the geometric relationship in Figure

So the following equation can be obtained:

For the convenience, let

And also set

Here, the physical meaning of

Substitute (

There are three unknowns in (

In order to obtain the polynomial, we let

According to (

To derive a univariate equation in

From (

Amplify (

We also have (

To get the nontrivial solution of (

From the appendix and (

As an example, we consider a 3-DOF CDWTM with the following initial structural parameters, the vertices vectors of the base are

Solving the equation, the eight sets of Rodridgues’ parameters can be achieved in Table

Eight sets of Rodridgues’ parameters.

1 | |||

2 | |||

3 | |||

4 | |||

5 | |||

6 | |||

7 | |||

8 |

According to (

The eight corresponding orientations (Unit : Degree).

1 | |||

2 | |||

3 | |||

4 | 12.3115 + 8.6638 | ||

5 | |||

6 | |||

7 | |||

8 |

Next we will demonstrate the validity of the analytic forward kinematics by the numerical example of inverse kinematics. Let the initial orientations of the scale model be zero, the corresponding vertices vectors of the moving platform are

With the help of

From the above equation, we have

So the lengths of the three cables are the norms of vectors

The inverse kinematic results are the same with the initial structural parameters of the forward kinematics, which verifies that the analysis of forward kinematics is correct.

This paper presents the kinematics analysis method of a novel 3-DOF cable-driven parallel mechanism used in wind tunnel test, and then we employ elimination method to solve the analytic forward kinematics of the mechanism by using of Rodridgues’ parameters, so an eighth polynomial in one variable is derived finally. A numerical example is included to verify the effectiveness and accuracy of the developed algorithm for real-time computation and control.

We have the following:

This work was Supported by the National Defense Pre-Research Foundation of China.