Kinematics, Workspace, and Singularity Analysis of a Parallel Robot With Five Operation Modes

Abstract

Most multi-mode parallel robots can change operation modes by passing through constraint singularities. This paper deals with a comprehensive kinematic study of a 3-DOF multi-mode 3-PRPiR parallel robot developed at Heriot-watt University. This robot is able to reach several operation modes without crossing any constraint singularity by using lockable Pi and R joints . Here a Pi joint may act as a 1-DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation mode and four 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation mode are dealt with in detail. The joint space and workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. It is shown that the robot is able to change assembly mode in one operation mode by passing through another operation mode. IntroductionReconfigurable Parallel Manipulators (PMs), such as multi-mode PMs [1][2][3][4][5][6][7][8][9][10][11][12], have received much attention from a number of researchers in the past decade [13]. The main characteristics of multi-mode PMs include [7-9]: a) fewer actuators are needed for the moving platform to realize several specified motion patterns; and b) less time is needed in reconfiguring the PM since there is no need to disassemble the PM in the process of reconfiguration.A number of interesting multi-mode PMs have been proposed, such as multi-mode PMs with a 3-DOF (degrees-offreedom) translational mode and a 3-DOF planar mode or a 4-DOF 3T1R mode [7,8], PMs with two 3T1R (also Schönflies motion) operation mode which has three translational DOF and one rotational DOF operation modes [4], PMs with two 2T1R operation modes [5,6], and 2-DOF 3-4R PMs with both spherical translation mode and sphere-on-sphere rolling mode [9]. References [14,15] show 4-DOF 3T1R PMs that have an extra 2-DOF or 3-DOF motion mode in addition to the required 4-DOF 3T1R motion mode. It is noted the metamorphic PMs based on reconfigurable U (universal) or S (spherical) joints [16,17] and the multi-mode PMs with lockable joints [18,19] are in fact kinematically redundant PMs in nature and do not belong to multi-mode PMs that this paper focuses on. In addition, several methods have been proposed [14,15,[19][20][21][22][23][24][25] to the reconfiguration analysis of multi-mode PMs for identifying all the operation modes and the transition configurations of a PM.

Reconfiguration Analysis of a 3-DOF Parallel Mechanism

“…Future work will focus on the optimization of this multi-mode PM and developing a prototype able to switch between the different modes by eliminating the constraint singularity. The main idea is to use lockable Pi (planar parallelogram) and R joints as proposed in Reference [26].…”

Modeling in Two Configurations of a 5R 2-DoF Planar Parallel Mechanism and Solution to the Inverse Kinematic Modeling Using Artificial Neural Network

“…The relationships between rotation parameters and complex number components are: shown in Table III, were generated using equations ( 29) and (31). This table shows three columns of interest: the linear path with 100 points (only 6 shown), the response of the trained neural network for the inverse problem, and the response of the Newton-Raphson method (see Figure 12).…”

“…To provide data for the training of a neural network, it is necessary to model the movements of robots or mechanisms to generate mathematical models through which it is possible to formulate inverse and direct kinematic problems. Traditionally these models are built using only one analysis configuration [27,28,29,30,31], limiting the motion relationships between the links that make up a robot. It is necessary to propose new modeling methods that consider two analysis configurations to systematize the rotations or translations that the actuators will perform and generate the mathematical models to raise and solve the kinematic problems associated with robots.…”

Actuation Spaces Synthesis of Lower-Mobility Parallel Mechanisms Based on Screw Theory

“…Assuming that the radius of the circumscribed circle of the fixed platform is 92.38 mm, and the circumscribed (16) circle of the movable platform is 57.74 mm, the movement range of the prismatic pair is 120-195 mm.…”

“…Improper actuator selection or placement in a flexure PM may cause additional errors, such as parasitic errors and even lead to actuation invalidity or redundancy [13]. In addition, it may cause interference [14], actuator singularity [15], and different driving modes that could affect the workspace [16], stiffness characteristic [17], and motion/force transitivity performance [18] in a rigid PM. When selecting and placing actuators, the moving pairs or frame pairs should be selected for convenience in practical application.…”