Abstract
In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.
Highlights
The direct kinematics problem is the problem of finding the actual position and orientation, known as pose, of the moveable manipulator platform with respect to the fixed base platform from the active joints’ coordinates
In order to avoid using the linear actuators’ lengths for solving the direct kinematics, we proposed a new sensor concept where the manipulator platform’s pose can be uniquely determined from the orientations provided by three inertial measurement units (IMUs) that were placed on top of the manipulator platform as well as on two of the linear actuators [24,25,26]
As the quality of the formulation’s results mainly depends on the quality of the measured linear actuators’ orientations, in this paper, we investigate the accuracy of our concept under static as well as dynamic conditions by performing several experiments on a new, specially designed prototype of a general planar 3-RPR parallel mechanism
Summary
The direct kinematics problem is the problem of finding the actual position and orientation, known as pose, of the moveable manipulator platform with respect to the fixed base platform from the active joints’ coordinates. For the general planar 3-RPR parallel mechanism, where three linear actuators, that is, active prismatic joints (P-joints), connect the passive revolute joints (R-joints) of the fixed base platform with those of the moveable manipulator platform, shown, up to six different poses of the manipulator platform are possible for a given set of linear actuators’ lengths These different poses that solve the direct kinematics problem are known as assembly modes. Due to the simple inverse kinematics of the general planar 3-RPR parallel mechanism with a unique solution, the linear actuators’ lengths can be directly calculated when the manipulator platform’s pose is known This allows to use other coordinates that are more suitable for solving the direct kinematics problem and, afterwards, calculate the linear actuators’. Orientation angles are denoted as φ1 , φ2 and φ3 and correspond to the angle between the x-axis and the first, second and third linear actuator, respectively
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