2-DOF Planar Parallel Manipulator Research Articles

Design and analysis of a novel 3-DOF planar parallel manipulator with two kinematic chains

In this work, to enlarge the workspace, a novel 3-DOF planar parallel manipulator (PPM) with two identical RRR kinematic chains is proposed, and this manipulator has a significant advantage in orienting the moving platform (MP) across a wide range of angles. Resorting to the closed-loop vector approach, the inverse position equation and Jacobian matrix of the novel manipulator are established. Payload performance, dexterity performance, and singularity of the proposed manipulator are analyzed based on the Jacobian matrix. To investigate the distribution characteristics of the constant orientation workspace, orientation workspace, and reachable workspace of the proposed manipulator, a numerical discretization method is employed. Under the same working mode and structural parameters, constant orientation workspace and reachable workspace comparisons between the proposed manipulator and another two traditional PPMs are conducted. Focused on three kinds of performance indices, link lengths optimization of the proposed manipulator is carried out. A 4-DOF pick-and-place equipment is fabricated, and the rotational and translational capabilities are verified based on two examples.

A Novel ANSMC Algorithm for Tracking Control of 3-DOF Planar Parallel Manipulators

A Novel ANSMC Algorithm for Tracking Control of 3-DOF Planar Parallel Manipulators

Trajectory Planning and Motion Control Schemes for 2DoF Planar Parallel Manipulator Biglide Type with Elastic Joints: A Comparative Study

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PZT Actuators’ Effect on Vibration Control of the PRRRP 2-DOF Flexible Parallel Manipulator

Thanks to their advantages over rigid ones, interest for lightweight parallel manipulator was increased. Besides, structural flexibility effects at high operational speeds are more significant. Thus, developing an appropriate model for the assessment of the dynamic properties of flexible mechanisms and linkages to gain effective vibration control will raise high demand. Therefore, this paper represents the dynamic and kinematic modeling using the assumed mode method and first-type Lagrange equations of the 2-DOF planar parallel manipulator with two flexible links. To truly predict vibrations of the manipulator without any major simplifying assumptions, nonlinear dynamic modeling, which thoroughly attempts to represent the flexible behavior of the links, is considered. As a result, an active damping approach is being studied with PZT actuators. The results show that this approach is effective in damping the vibrations of the links that give accurate trajectory control.

Dynamics and control of a 3-DOF planar parallel manipulator using visual servoing resolved acceleration control

This paper proposes the visual servoing resolved acceleration control scheme applied to a 3-degree of freedom (DOF) planar manipulator, which aims to reduce computational loads of the feedback control loop and the tracking errors of the end-effector in the conventional resolved acceleration control scheme. The computation loads are increased due to the calculations of the direct kinematics and the velocity inversion in the feedback control loop. The tracking errors of the end-effector are increased due to low-accuracy encoders, gearbox backlashes, and manipulator flexibility, etc. The proposed scheme incorporates a visual system, which directly captures the position of the end-effector instead of calculating the direct kinematics and the velocity inversion. Due to the requirement of inverse dynamics in the proposed scheme, the transformation of the Jacobian matrices between the passive and active links is imposed to the Euler-Lagrange’s equation so as to derive dynamic equations. In order to show the control performances, three existing torque-based control schemes are also applied to the manipulator. This study investigates the numerical simulations and the experimental validations, and the results show that the proposed scheme can reduce the computation loads and the tracking errors of the end-effector to compare with the three existing schemes.

End-effector positioning due to joint clearances: A comparison among three planar 2-DOF parallel manipulators

This paper develops a model for studying the effect of joint clearances on the end-effector’s loci for planar parallel manipulators with 2 degree-of-freedom (DOF). The condition for developing end-effector loci equations with respect to the joint clearance relies on the fact that at least one point of contact is always presented in each joints. The motivation of this work lies in the fact that the proposed procedure allows the study of parallel manipulators that can be considered as design concepts for developing an x-y cutting table for a textile industry. Numerical simulations enable to compare three 2-DOF planar parallel manipulators architectures: i) 2-RRR, ii) 2-RPR, and iii) 2-RPR. A Monte Carlo simulation allows us to find the area of possible end-effector locations for a specific value of clearance. Also, the equations allow us to find the largest distance from the desired location to the one obtained considering clearance. Findings shed some lights on establishing which parallel manipulator is less affected to joint clearance.

Development master arm of 2-DOF planar parallel manipulator for In-Vitro Fertilization

Micromanipulator is a mechanical device used for manipulating miniature objects in the order of micron. It is widely used in In-Vitro Fertilization (IVF) in which sperms will be held in a micro-needle and penetrate to an oocyte for fertilization. IVF needs to be performed by high skill embryologists to control the movement of the needle accurately due to the lack of tactile perception of the user. Haptic device is a device that can transmit and simulate position, velocity and force in order to enhance interaction between the user and system. However, commercially available haptic devices have unnecessary degrees of freedom and limited workspace which are inappropriate for IVF process. This paper focuses on development of a haptic device for using in IVF process. It will be used as a master arm for the master-slave system for IVF process in order to enhance the ability of users to control the micromanipulator. As a result, the embryologist is able to carry out the IVF process more effectively with having tactile perception.

A new neural gas network approach for obtaining the singularity-free workspace of 3-DOF planar parallel manipulators

This paper proposes a new extension of the Growing Neural Gas Network, called the Progressive Growing Neural Gas Network (PGNGN), for the application of kinematic investigation of parallel mechanisms, with more emphasis on the singularity-free workspace determination. In fact, PGNGN leads to a general approach in order to obtain the topology of the workspace. In this algorithm, the network starts to grow by taking into account new data points close to its border neurons by resorting to the so-called boundary data generation procedure. By considering singularity loci expression, the separated parts are detected and each part will pursue learning, adding units and connections, until a given performance criterion will be reached. Finally, after finding cavities, if any exists, the maximal circle for each part of the workspace is found. A graphical user interface (GUI) is developed providing the users with easy access to the important parameters in which the singularity-free workspace of three planar three-degree-of-freedom (3-DOF) parallel mechanisms are investigated in which two of them, namely, 3-RRR and 3-PRR parallel mechanisms, are among the most complicated parallel mechanisms due to their highly nonlinear and complicated singularity loci expressions. Results reveal the applicability and reliability of the proposed PGNGN-based approach for obtaining the singularity-free workspace of planar parallel mechanisms.

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR-PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined. HighlightsFour working modes are analyzed and the optimal mode for painting a long rocket fairing with conical surface is determined.Dynamic performance indices are designed on the basis of acceleration vector of the moving platform produced by a unit actuated force.The index not only can evaluate the accelerating performance, but also can reflect the isotropy of accelerating performance.

Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory

This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

A geometrical workspace calculation method for cable-driven parallel manipulators on minimum tension condition

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.

Workspace Analysis and Optimization of 3-RRR Planar Parallel Manipulator

Predicting shape and finding out exact area of the workspace of 3-DOF planar parallel manipulator having three rotary joints has been a research topic for long time. Optimal design based on such calculations provides a conclusive design methodology. In this work, geometrical method is used o get the exact shape of the workspace and expression of area for the shape obtained. The 3-DOF parallel manipulator is treated as a combination of three independent serial manipulators and its workspace as the common intersection area of these three serial manipulators. The three workspaces are then translated by length equal to radius of the end effecter and the common intersection area is obtained as the workspace of the parallel manipulator under study. The area is determined using the mathematical expression for the shape obtained. Based on direct search algorithm, a methodology is developed to optimize the area. Thus, following, this methodology, an user with specification of area of the workspace can be provided with an optimized parallel manipulator taking into account the inventory of link lengths and the cost of the links.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,”Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

Inverse dynamics and control of a 3-DOF planar parallel (U-shaped 3-PPR) manipulator

This paper addresses the inverse dynamics of three degrees of freedom (DOF) U-shaped planar parallel manipulator having three legs consisting of prismatic-prismatic-revolute (PPR) joint arrangement in which each leg has one active prismatic joint. This paper also proposes a proportional-derivative (PD) like adaptive sliding mode control combined with a disturbance observer for the motion control of the proposed manipulator. Using this control scheme, the controlled robotic manipulator is transformed into decoupled dynamics, and thus the motion performance is very convenient to quantify. Based on Lyapunov like argument the global asymptotic stability of the proposed closed loop system is proved. Real time experiments performed on the in-house fabricated prototype of the proposed manipulator are provided to substantiate the effectiveness and the improved performance of the proposed controller. The proposed controller performances are also compared with traditional controllers such as proportional integral derivative (PID) controller, sliding mode controller (SMC) and computed torque controller (CTC) Inverse dynamics of a 3-DOF planar parallel robot (3-PPR) is presented.A robust tracking controller with disturbance compensation has been introduced.Effectiveness of the controller has been demonstrated with prototype experiments.A comparative study of the proposed and existing controllers has been performed.

Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation

A new robust nonlinear controller is presented and applied to a planar 2-DOF parallel manipulator with redundant actuation. The robust nonlinear controller is designed by combining the nonlinear PD (NPD) control with the robust dynamics compensation. The NPD control is used to eliminate the trajectory disturbances, unmodeled dynamics and nonlinear friction, and the robust control is used to restrain the model uncertainties of the parallel manipulator. The proposed controller is proven to guarantee the uniform ultimate boundedness of the closed-loop system by the Lyapunov theory. The trajectory tracking experiment with the robust nonlinear controller is implemented on an actual planar 2-DOF parallel manipulator with redundant actuation. The experimental results are compared with the augmented PD (APD) controller, and the proposed controller shows much better trajectory tracking accuracy.

Non-singular transitions between assembly modes of 2-DOF planar parallel manipulators with a passive leg

In the field of parallel manipulators, the possibility of changing assembly mode without passing through a singular configuration is well known. This kind of transitions was studied in detail for planar 3-DOF manipulators. This paper focuses on 2-DOF parallel manipulators actuated by two RRR legs and constrained to a 2-DOF motion by a passive leg. It first shows that when the platform movement is constrained to rotations and translations along a single direction, nonsingular assembly mode transitions are possible. The direct and inverse kinematic problems of the mechanism are solved. The singularity conditions are written in explicit form and geometrically interpreted. Numerical examples of nonsingular assembly mode transitions are then given. Subsequently, the paper proves that if the platform is instead constrained to translational motions, nonsingular assembly mode transitions become impossible. Remarks on the generalization of the results to a wider class of 2-DOF planar manipulators are finally given.

Workspace quality analysis and application for a completely restrained 3-Dof planar cable-driven parallel manipulator

With the advantage of large workspace, low energy consumption and small inertia, the cable-driven parallel manipulator (CDPM) is suitable for heavy workpieces in rapid velocity and acceleration. We present a workspace analysis approach to solve force and torque equilibriums of completely restrained CDPMs. By this approach, not only the distribution but also the value of tensions driven by cables is investigated together. Two new indices, all cable tension distribution index (ACTDI) and area of the global quality workspace (AG) are proposed to evaluate the quality of the workspace. By concentrating on the workspace and its quality combined with the tension characteristics, these criteria are used to determine the optimal workspace in CDPMs. To verify the capacity of the proposed method, simulation examples are presented and the results demonstrate the approach’s effectiveness. In the end, the dimensional design for a planar CDPM is discussed with the indices of workspace quality.

Kinematic Analysis of a 2-DOF Planar Parallel Manipulator with Automated Selective Activation Mechanism to Avoid Singularities

Parallel Manipulator has lot of applications in areas like flight/automobile simulators, earthquake simulators, milling machine, etc. Main disadvantage of parallel manipulator is the presence of singularities within the workspace. Due to this, entire workspace of a parallel manipulator cannot be used effectively. To overcome this disadvantage, an automated selective activation mechanism is proposed, designed and fabricated using solenoids, gear train and belt drive arrangement. By using this mechanism interior singularity are crossed and this enables the user to utilize the entire workspace. Selective activation mechanism with automation ability is designed in such a way that, depending on activation of solenoid, active joint of manipulator changes from one position to another, which subsequently changes the singularity curves. By changing active joint positions, 4 ways of operating manipulator are identified. For all type of operations, singularity curves are plotted using MATLAB.

Force optimization of planar 2-DOF parallel manipulators with actuation redundancy considering deformation

Internal force distribution is one of the most important issues for redundantly actuated parallel manipulators. This article presents a novel method for optimizing internal force to minimize the deformation of key components in a parallel manipulator. The dynamic model is first derived, and then an objective function is proposed by giving different weights on internal forces of different components based on its flexibility. The deformation of the component with big flexibility is minimized. A planar 2-DOF parallel manipulator with actuation redundancy is taken as an example to validate the force optimization method. The simulation results show that the deformation of the manipulator with the force optimization method proposed in this article is smaller than that with the traditional method to minimize the norm of driving forces. Thus, the manipulator precision can be improved.