Kinematic accuracy research of a novel six-degree-of-freedom parallel robot with three legs
Introduction
Parallel robots are increasingly being used for precision positioning in industrial robot applications, and a number of them are essential for achieving high functionality of products and to enhance productivity [1], [2]. The demand for high precision tasks for parallel robotic systems is continuously growing, to the point that designing manipulators granting the prescribed accuracy is becoming a critical issue [3], [4]. Therefore, it is necessary and important to develop an effective and accurate approach to predict the influences of the pose (position and orientation) error and improvement of the kinematic accuracy of parallel manipulators [5], [6].
The pose error of a manipulator is defined as the deviation error between the pose of the actual configuration and that of the ideal configuration. Due to the existence of servopositioning errors, dynamic effects, and geometric tolerances, such as assembling, loading, manufacturing tolerances, and the mechanical clearance between the pairing elements of kinematic chains are considered predictable due to their deterministic influence on the pose deviation. As shown in Fig. 1, the nominal configuration of the end-effector is represented by B relative to the base frame A. Suppose that with a pose error, the relative kinematic deviation error can be defined from the actual body B′ to the base frame A. Meanwhile the input errors of the active-joints and the unexpected displacements of the manipulator's end-effector will be inevitable in the practical applications of the parallel manipulator.
Among the above error sources, three types of error sources in the position and orientation of a parallel robot can be considered in this study. First, the manufacturing tolerance error arises from machining the individual links and from the end-effector deflections caused by the cutting forces [4]. To solve this problem, one main method is to improve the manufacturing process to eliminate these errors by applying high-precision processing equipment. However, this could be quite costly and unattainable with the current tolerance limits. Conversely, many methods have been proposed to determine the manufacturing errors and account for them in the robot software [7], [8], [9], [10].
Second, the mechanical clearance is often a needed, because the clearance is also essential for correct functioning and easy assembly of the underlying mechanism [11], [12], [13]. The error sources probability induced by the great number of limbs and passive joints. The existence of the mechanical clearance will introduce extra degree-of-freedom displacements between the pairing elements in kinematic chains and contributes directly to the position and orientation errors of the mechanism. Much research has been devoted to the study of mechanical clearance and its effect on the pose accuracy of a parallel mechanism [14], [15], [16], [17]. From these studies, the kinematic relationship between the displacements in each clearance-affected joints is important.
Third, apart from the manufacturing error and the mechanical clearance, active-joint errors are the most significant source of errors [1]. They can be induced by non-perfect assembling of different active elements and arise in shifting and/or rotation of the frames associated with different components, which normally are assumed to be matched and aligned [29]. Many researchers have studied the accuracy analysis of parallel manipulators with active-joint errors during the past two decades [18], [19], [20]. The classical method consists of considering the first order approximation that maps the active-joint errors to find the largest maximal pose error of the end-effector. However, when a robot involves both translational and rotational kinematic joints, it is difficult to establish an effective modelling for the output error vector with physical interpretations [10].
Among the existing literature, the main method in most works is to determine the sensitivity of the accuracy of the end-effector to the maximum position and maximum orientation errors over a given portion of the workspace or at a given nominal configuration [1], [22]. In addition to the significant improvements over conventional technology, several performance indices have been developed and used to evaluate the accuracy of the robots [23], [24], [25]. The common conclusion is the sensitivity of the accuracy of the end-effector to different types of errors. Moreover, all of the existing research investigated the accuracy performance based on one or two aspects. None of them simultaneously investigated the uncertainty effects of these three error sources in a unified manner.
In order to improve the accuracy of the kinematic model, there exists a number of sophisticated calibration techniques that are able to identify the errors between actual and nominal kinematic parameters [26], [27]. Calibration methods can be classified into two categories, a direct calibration method and a kinematic calibration method [28], [29]. External devices are required to measure pose of the end-effector accurately in the direct calibration. The kinematic calibration methods have the advantages of removing the dependence on pose measurement, it uses the residuals between values measured by external devices and values calculated by kinematic relationships at all measured positions, this method is more complicated than the calibration method. Consequently, these types of errors can be efficiently compensated by either by adjusting the controller input or by modification of the kinematic parameters.
In this paper, we propose a method in which we follow a detailed mathematical proof that provides important insight into the kinematic accuracy of the pose of the platform of a new 6-DOF parallel robot. We propose an error prediction model, which combines the effect of the manufacturing errors, mechanical clearance and active-joints errors on the pose of the platform of a new 6-DOF parallel robot. The compensation data will be obtained by calculating the input through the errors model and the mathematical model. The controller of control unit can modify the stroke input by calculated compensation data to guarantee precise pose of the end-effector.
The remainder of this paper is organized as follows. Section 2 briefly outlines the generalized kinematic mapping of constrained motions of the proposed robot. Section 3 presents the method used for the analysis of the orientation and position errors. Section 4 calculates the errors by using a numerical example. The results are presented via a set of experiments in Section 5. In the end, a short conclusion is drawn in Section 6.
Section snippets
Nominal kinematics of the TLPM
The 3-D architecture of the TLPM is presented in Fig .2. This robot has a parallel kinematic structure with three identical branches connecting the fixed platform to the moving platform. Each branch is configured by an active revolute (R) joint, two passive R joints, an active prismatic (P) joint and a universal (U) joint. This design has six degrees-of-freedom, namely three rotations around the x, y and z axes and three translations along the x, y and z directions. The six active joints are
Pose error of the TLPM
According to the constraint kinematics of this robot, the error sources can be divided into three main categories: (1) location errors of the U joints, (δpU, δΩU)i. These errors are caused mainly by imperfect geometry and manufacture as well as the assembly and thermal growth of the base and of the platform. (2) Clearance originating at kinematic joints. Theoretically, the shaft is constrained to having one rotation about it relative to the bearing. However, due to the inaccuracies of geometry
Distribution of the error within the workspace
As addressed in the above analysis, we will extend the accuracy analysis of manipulators with the location of the U joint, passive joint clearance and active joint errors, and then establish a procedure to predict the exact output error bound of the TLPM with location uncertainties, joint clearance and input uncertainties. To simplify the presentation of the results, the pose error is split into a position error and an orientation error within a certain workspace.
Experiment
To examine the effectiveness of the methodology, the experiment was performed in a laboratory. As shown in Fig. 13, the fixed coordinate system (FCS) was attached to the centre of the base platform, its z axis is defined as the axis in the direction from o to p, and the x axis is defined as the axis in the direction from o to q1; the moving coordinate system (MCS) was located at the upper surface centre of the moving platform; its z′ axis is parallel to the vector op, and the x′ axis is
Conclusions
A novel 6-DOF parallel robot TLPM was briefly described in this article; the main contributions of this article are as follows: a basic issue of mechanisms, i.e., the kinematic accuracy, was proposed in the TLPM research field. According to the method of calculation of the kinematic accuracy process, we investigated the effect of the location of the U joint errors, clearance and driving errors, overcoming the unreasonable phenomena of ‘complete satisfaction or not’ of traditional methods and
Acknowledgements
This project is partially supported by the National Basic Research Program of China (973 Program, Grant No. 2013CB035501).
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Mechanical Building, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Shanghai 200240, PR China.