2-DOF Planar Parallel Manipulator Research Articles

Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool

SUMMARYThis paper addresses the dynamic dexterity of a planar 2-degree of freedom (DOF) parallel manipulator with virtual constraint. Without simplification, the dynamic formulation is derived by using the virtual work principle. The condition number of the inertia matrix of the dynamic equation is presented as a criterion to evaluate the dynamic dexterity of a manipulator. In order to obtain the best isotropic configuration of the dynamic dexterity in the whole workspace, two global performance indices, which consider the mean value and standard deviation of the condition number of the inertia matrix, respectively, are proposed as the objective function. For a given set of geometrical and inertial parameters, the dynamic dexterity of the parallel manipulator is more isotropic in the center than at the boundaries of the workspace.

Dynamic design of a planar 3-DOF parallel manipulator

The design of a planar three-degree-of-freedom parallel manipulator is considered from a dynamic viewpoint.Firstly,the dynamic equations of the planar three degree-of-freedom parallel manipulator based on the Lagrange equation are presented.Then, three different design measures are established for the first time.For example,selection proper balancing masses are added to the system for eliminating the gravity and most of the coupling terms from the dynamical equations.These design measures are useful for improving dynamic properties,controllability,stability and accuracy of the mechanism.Finally,an example is given in order to illustrate the effect of greatly reducing the required actuator torques and consumed energy.The analysis presented,could provide necessary information for dynamic performance analysis,optimization design and control of the parallel mechanism.The method can be easily extended to the dynamic analysis and design of other multi-linkage and multi-degree-of-freedom mechanisms.

Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

Optimal Kinematic Design of a 2-DOF Planar Parallel Manipulator

Closed-form solutions were developed to optimize kinematics design of a 2-degree-of-freedom (2-DOF) planar parallel manipulator. The optimum design based on the workspace was presented. Meanwhile, a global, comprehensive conditioning index was introduced to evaluate the kinematic designs. The optimal parallel manipulator is incorporated into a 5-DOF hybrid machine tool which includes a 2-DOF rotational milling head and a long movement worktable. The results show that the planar parallel manipulator-based machine tool can be successfully used to machine blades and guide vanes for a hydraulic turbine.

Auto-calibration of a redundant parallel manipulator based on the projected tracking error

Utilizing the projected tracking error of the redundant joint angles, we studied the calibration problem of the sensor zero positions of a planar 2-dof parallel manipulator in this paper. Based on the study of the relationship between the projected tracking error of the joint angles and the error of the sensor zero positions, a new error function is proposed for the calibration of the sensor zero positions of the parallel manipulator. It is proved that the error function is robust to the measurement error of the joint sensors, so accurate calibration results can be obtained by minimizing the error function even if the measurement of the joint angles is not accurate. With a simple searching strategy for the minimal value of the error function, we designed an auto-calibration procedure and verified the validity of the calibration procedure through real experiments on a real redundant planar 2-dof parallel manipulator.

Kinematics and optimization of 2-DOF parallel manipulator with revolute actuators and a passive leg

In this paper, a 2-DOF planar parallel manipulator with two revolute actuators and one passive constraining leg. The kinematic analysis of the mechanism is analytically performed: the inverse and forward kinematics problems are solved in closed forms, the workspace is derived systematically, and the three kinds of singular configurations are found. The optimal design to determine the geometric parameters and the operating limits of the actuated legs is performed considering the kinematic manipulability and workspace size. These results of the paper show the effectiveness of the presented manipulator.

Dynamic analysis of the 2-DOF planar parallel manipulator of a heavy duty hybrid machine tool

This paper focuses on the dynamic characteristics of the two degree-of-freedom (DOF) planar parallel manipulator of a heavy duty hybrid machine tool. The Newton-Euler approach is employed to derive the inverse dynamic equation of the parallel manipulator. According to the motion planning of the cutting tool, dynamic simulation without cutting force is performed, and the ratio of the masses of counterweights to that of moving parts (not including the counterweight) is optimized. It demonstrates that the manipulator which is designed with over constraint can improve the dynamic behaviour. Furthermore, the cutting force model for face milling is introduced and the dynamic simulation with the dynamic cutting force is carried out. Simulation shows that the oscillation of cutting force is one cause of the vibration of the machine tool in the milling process. In the detailed design, some modification in the structure of the machine tool is made to suppress the vibration.

ANALYSIS OF PERFORMANCES OF PLANAR 2-DOF PARALLEL MANIPULATOR WITH ACTUATION REDUNDANCY

As the subject investigated, the planar 2-DOF parallel manipulator with actuation redundancy is treated as non-dimensional structure. The physical model of the solution space, which can reflect the scope in which the geometric parameters change, is presented. Kinematic equation is established, solution to inverse kinematics and velocity Jacobian matrix are given. The global performance indices of the manipulator are defined and calculated. The relationship between link lengths and global performance indices, such as condition number of Jacobian matrix, payload and stiffness are discussed; corresponding atlases are plotted in the physical model of the solution space. According to these atlases, the distribution rule of the three performance indices in the physical model of the solution space is concluded; the better dimension scope of each performance index is made out respectively. Finally, when the three performance indices are considered as the optimum indices simultaneously, the optimal dimension scope is obtained by synthesizing the three dimension scopes. These atlases give a possible path to optimize manipulator using kinematic performance indices. This method also provides a simple and effective way for designing parallel manipulator using computer-aided.

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity.

Optimal Multiple Orientation Synthesis Of APlanar Parallel Manipulator Performed ForDifferent Prescribed Output Workspaces

The optimal multiple orientation synthesis methodology presented in this paper is aimed at determining designs of a three degrees of freedom (3-dof) planar parallel manipulator, so that the manipulator reaches, with optimal conditioning, all points in a prescribed output workspace for multiple specified constant (fixed) orientations of the manipulator platform. The optimum conditioning with respect to the manipulator design variables is obtained by minimizing the condition number over the enclosed prescribed physical workspace for all the different prescribed discrete fixed orientations. The proposed optimization methodology produces convincing results, indicating it to be a stable and efficient numerical method for designing planar parallel manipulators.

2815 射出成形3PRR連節からなる3自由度平面パラレルマニピュレータの出力節の振動特性(S59 機構の開発とシミュレーション)

A new surface mount system with arrangement of miniature manipulator was proposed for use in system down sizing. The new surface mount system consists of a molded pantograph and 3DOF planar parallel manipulator with 3PRR link chain. In this research, we investigated the vibration characteristics of the planar parallel manipulator. This manipulator mechanism consists of large-deflective hinges and links made by the injection molding machine. Its material is Polypropylene (PP). First, we measured the maximum amplitude and frequencies of the output link of the manipulators by impact test. Next, we made the manipulator with 3 linear input motion part with a rotary DC motor and lack-and-pinion. Moreover, we made clear the vibration characteristics of the manipulator by experiments comparing with the above impact test results.

Determination of dexterous workspace of planar 3-DOF parallel manipulator by auxiliary linkages

Determination of dexterous workspace of planar 3-DOF parallel manipulator by auxiliary linkages

Methodologies for the optimal design of parallel manipulators

AbstractIn this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two different strategies, resulting in two different types of optimization problem are considered. The first strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two specific formulations of the constrained problem are proposed. The first constrained problem simply aims to fit the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well‐conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2‐dof planar parallel manipulator, and the final formulation is also applied to a 3‐dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators. Copyright © 2003 John Wiley & Sons, Ltd.

Kinematics and dynamics of a general-purpose, parallel, compliant micromanipulator

Kinematic and dynamic modelling of a three-degrees-of-freedom (3DOF) planar parallel manipulator is presented in this paper. An equilateral triangle forms the output stage of the mechanism, and three driving structures, connected via three links, provide stroke magnification to the output stage. Aiming at achieving micromotions, this manipulator is developed using compliant material. In order to reduce assembly errors, a monolithic structure is adopted in this design. Hence, the joints in this mechanism are all flexural hinges. Since the masses and moments of inertia can be neglected in this lightweight micromanipulator, and the joint resistances are greatly increased owing to the flexure of the joints, new problems arise in the design and modelling of such a mechanism. The results presented in this paper will provide useful information for the design and applications of parallel, compliant micromanipulators.

The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators

The workspace for robotic manipulators is a very important issue for optimum design of robots, especially for parallel manipulators. The relationship between the shapes of workspaces and the link lengths of manipulators is very close. In this paper, 3-DOF planar parallel manipulators (3-DOF PPMs) are classified; various of shapes of the workspaces are presented; the relationships between the shapes of the workspaces and the link lengths of each of the classifications are presented. The results of this paper are useful for the designers not only to understand the distribution of characteristics of the workspaces for various link lengths of 3-DOF PPMs, but also to optimize the manipulators.

A general dynamic model for a large-scale 2-DOF planar parallel manipulator

In this work a new concept of designing two degree of freedom (2-DOF) planar parallel manipulators (PPMs) is presented. With this design the manipulator's workspace can be increased by increasing the number of cells in the manipulator. A general dynamic model is formulated for the manipulator with any number of cells. The model is adapted for SCARA and ADEPT configurations, and a new approach for balancing these type of manipulators is proposed.

A simplified approach for obtaining the workspace of a class of 2-dof planar parallel manipulators

This paper presents a method for generating the reachable workspace of a class of planar two-degree-of-freedom (dof) end-effector-type manipulators. This class is based on six planar linkages with five links and five joints, revolute and/or prismatic. A common set of two quadratic equations is presented that determine the workspace of all the class as a function of the input motions of the manipulator under study. The quadratic equations involve only the Cartesian coordinates ( x, y) of the operation point. Thus, the formulation is governed by the analytical solution of a well known second order equation and the inverse kinematic problem is not required. Because of the simplicity of the involved equations, an algorithm can be easily implemented on a computer program. Examples of generated workspaces for all the class are given to illustrate the proposed approach.

Transition of Output Error Distribution caused by Joint Clearances around 3-DOF Planar Parallel Manipulator.

Planar parallel manipulators with three degrees of freedom are instruments adequate enough to complete planar microstage mechanisms. Because the planar parallel manipulators have high enough structural stiffness and whole of their actuators are allowed to be arranged on a base with ease. In this paper, 3-DOF planar parallel mechanisms with revolute joints and strict output errors are analyzed theoretically and experimentally in consideration of joint clearances. In the case where large joint clearances are found, for example, as a result of the above analysis, in the joint clearances in the mechanisms constructed by surface micromachining techniques, a magnification of output error areas produced by transition from a direct kinematic solution to the other one is liable to occur and output errors are made greater in the areas where transmission index (TI) remains small.