Symmetrical Parallel Manipulators Research Articles

Kinematics Performance Analysis and Optimization of Symmetrical Super-redundant Parallel Manipulators 6RPS

Kinematics Performance Analysis and Optimization of Symmetrical Super-redundant Parallel Manipulators 6RPS

Design of Fixed-Sequence Planar 5R Symmetrical Parallel Manipulators

Designing manipulation systems where the gripper has predetermined initial and final positions is an important practical consideration in modern robotics; in other words, achieving the objective of moving the payload along a non-imposed trajectory between two given positions, with the ability to change these positions periodically. One solution to the problem is to create a one-degree-of-freedom system with adjustable parts. This approach is considered optimal in terms of its simplified control and minimum energy expenditure. The merit of the solution is that manipulation systems of this type with cyclic control have only one actuator; the simple design and the control system improve the operational reliability of the mechanical system while greatly reducing the cost of it. The present work proposes a new design concept for a planar 5R symmetrical parallel manipulator. The aim of the proposed design principle is that the two input links of the manipulator are interconnected. The last one is determined in such a way that the initial and final positions of the gripper are ensured. Thus, the obtained mechanical system, having only one actuator, ensures the movement of the gripper between predetermined initial and final positions. The dynamics of the manipulation system, in particular the balancing of shaking force and shaking moment to reduce vibration in the frame, are considered in addition to the purely kinetic aspects. Numerical simulations are used to illustrate the proposed design concept.

Integration modeling and control of a 12-degree-of-freedom macro–micro dual parallel manipulator

Parallel manipulator systems with large workspace and high-accuracy positioning are attractive for a variety of accuracy engineering applications. In this article, a new 12-DOF macro–micro dual parallel manipulator is presented, which comprises a 6-PSU macro symmetrical parallel manipulator and a 6-SPS micro orthogonal parallel manipulator. This novel mechanism can not only realize a large range of movement but also accurate positioning. To achieve high-accuracy control, a macro–micro integrated model of the macro–micro dual parallel mechanism is proposed, including a mechanical system model and drive system model. Aiming at the trajectory planning for a multi-degree-of-freedom (DOF) manipulator, a smooth optimization trajectory planner for the 12-DOF macro–micro dual parallel manipulator is presented to realize smooth trajectory generation. A high-accuracy motion controller combining feedback and feedforward is developed based on the drive system model. Finally, the experiment well validates the correctness of the integrated model and motion control algorithm and reveals that the proposed mechanism is expected to be adopted into micro scale manipulations.

Acceleration analysis of 6-RR-RP-RR parallel manipulator with offset hinges by means of a hybrid method

In this work, the kinematics of a symmetrical hexapod parallel manipulator is investigated by means of Denavit-Hartenberg method and differential transformation method. When compared with a general Gough-Stewart platform, the limbs of the parallel manipulator are connected to the mobile and fixed platforms through offset hinges, rather than traditional spherical and universal hinges. Because the offset variable of the hinge axis are introduced by the offset hinge, the kinematics of the parallel manipulator studied becomes more complicated. The forward and inverse displacement analysis are approached by means of the Denavit-Hartenberg method. Then, the velocity and acceleration are analyzed using differential transformation method. The concise expression is obtained and can be easily translated into computer program. The derivation of acceleration analysis of the 6-RR-RP-RR parallel manipulator using the hybrid approach is novel in this research field. Finally, a numerical example is given and the numerical results are verified via co-simulation.

Mechatronics Design and Kinematic Analysis of SMA Spring Actuated Parallel Manipulator

Flexible parallel manipulators can be used as an orienting device because of their precise positioning ability and better stiffness. The flexibility to the manipulator induces challenges in the selection of actuator, sensors and control. The paper presents a novel mechatronics design of a flexible symmetric parallel manipulator with minimum number of actuators used as an orienting device. Shape memory alloy springs (SMA) are used as an actuator because of ease of integration and higher deflection. In order to avoid any contact type sensor which could affect the compliance of the manipulator, the position of SMA spring is calculated indirectly from the kinematic model with the end effector orientation data measured from IMU sensor. The complete experimental set up design including electrical and control circuitry is explained in detail in the work. Preliminary open loop test is conducted on the prototype to understand the SMA response to various current input and to verify the effectiveness of the kinematic model in the actuator length measurement. Closed loop control based on ON/OFF control is implemented in the controller and is tested for step input.

A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

Kinematics of the 4-RUU parallel manipulator generator of the Schönflies motion by means of screw theory

This work deals with the inverse–forward kinematic analysis of a symmetric parallel manipulator equipped with a rotary actuator generator of three independent translations and one rotation motion. The closure equations of the displacement analysis are easily formulated based on the unknown coordinates of two points embedded in the moving platform. The input–output equations of velocity and acceleration of the robot are systematically obtained through the reciprocal-screw theory. The pseudo-kinematic pairs that connect the limbs to the fixed platform and a passive kinematic chain connected to the robot manipulator eliminate the handling of rank-deficient Jacobian matrices, which is an undisputable advantage from the computational point of view. Furthermore, this strategy allows the use of the Lie algebra se(3) without the inherent restrictions associated with the limited mobility of the robot.

Forward Kinematics Solution Distribution and Analytic Singularity-Free Workspace of Linear-Actuated Symmetrical Spherical Parallel Manipulators

This paper presents a new kinematics model for linear-actuated symmetrical spherical parallel manipulators (LASSPMs) which are commonly used considering their symmetrical kinematics and dynamics properties. The model has significant advantages in solving the forward kinematic equations, and in analytically obtaining singularity loci and the singularity-free workspace. The Cayley formula, including the three Rodriguez–Hamilton parameters from a general rotation matrix, is provided and used in describing the rotation motion and geometric constraints of LASSPMs. Analytical solutions of the forward kinematic equations are obtained. Then singularity loci are derived, and represented in a new coordinate system with the three Rodriguez–Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are illustrated and forward kinematics (FK) solution distribution in the singularity-free zones is discussed. Based on this analysis, unique forward kinematic solutions of LASSPMs can be determined. By using Cayley formula, analytical workspace boundaries are expressed, based on a given mechanism structure and input actuation limits. The singularity-free workspace is demonstrated in the proposed coordinate system. The work gives a systematic method in modeling kinematics, singularity and workspace analysis which provides new optimization design index and a simpler kinematics model for dynamics and control of LASSPMs.

Design and transmission analysis of an asymmetrical spherical parallel manipulator

This paper presents an asymmetrical spherical parallel manipulator and its transmissibility analysis. This manipulator contains a center shaft to both generate a decoupled unlimited-torsion motion and support the mobile platform for high positioning accuracy. This work addresses the transmission analysis and optimal design of the proposed manipulator based on its kinematic analysis. The input and output transmission indices of the manipulator are defined for its optimum design based on the virtual coefficient between the transmission wrenches and twist screws. The sets of optimal parameters are identified and the distribution of the transmission index is visualized. Moreover, a comparative study regarding to the performances with the symmetrical spherical parallel manipulators is conducted and the comparison shows the advantages of the proposed manipulator with respect to its spherical parallel manipulator counterparts.

A geometric approach for the workspace analysis of two symmetric planar parallel manipulators

SUMMARYThe workspace is often a critical parameter for optimum design of parallel manipulators. Workspace shape and area are two important considerations under this. In this paper, 5-R and 3-RRR planar parallel manipulators having symmetric link lengths are considered for workspace analysis. Here, symmetric means that the lengths of the first and second links of the legs are the same in all branches. Workspace analysis for such manipulators is normally done in a nondimensional way. The determination of the workspace area is one of the important parameters in the optimum design of a manipulator, and the determination of the area in terms of nondimensional parameters is extremely difficult in the case of 3-DOF and higher-DOF manipulators. In this paper, a geometric method is presented to determine different workspace shapes and areas. Based on this, all possible shapes of workspace are presented for both 5-R and 3-RRR planar parallel manipulators. For each case, a geometrical relationship between the link lengths is determined. The geometric approach gives a closed-form expression for the area calculation, which is not possible when adopting a nondimensional approach. In addition, this approach provides relationships between workspace shape and area and link lengths.

Performance Analysis and Comparison of Planar 3-DOF Parallel Manipulators with One and Two Additional Branches

This paper constructs a symmetrical 3-DOF parallel manipulator with one and two additional branches, respectively. The conditioning, stiffness, velocity and payload indices are developed to compare the performance of the two parallel manipulators, one with one additional branch, and the other with two additional branches. The optimum performance region with desirable performance is investigated. The simulations show that the redundant manipulator with one additional branch has a larger optimum performance region with the given conditioning, velocity, payload and stiffness performance. The results are not only important for designers to design the 3-DOF parallel manipulator, but also helpful for researchers to determine how many additional branches are added to develop a redundant parallel manipulator.

Kinematics Analysis and Dimensional Synthesis of a Plane Symmetric 3-SPR Parallel Manipulator

Kinematics Analysis and Dimensional Synthesis of a Plane Symmetric 3-SPR Parallel Manipulator

Workspace Analysis and Going through Singularities of 5-Bar Symmetric Planar Parallel Manipulator by Automated Selective Actuation Mechanism

In this article‚ a new approach is presented to determine the various shapes of workspaces of 5 bar symmetric planar parallel manipulators. Here the shape of the workspace is determined by the number of ways the workspaces of the two serial manipulators intersect with each other. Geometric conditions are established in each case and area of each shape of workspace is determined in closed form. Singularity is another important consideration in the design of parallel manipulators. In this paper, an approach is presented to go through the singularity points using an automatic selective actuation mechanism. A prototype 5-bar planar manipulator is fabricated along with an automatic selective actuation mechanism demonstrating the manipulator going through the singularity points.

Optimal Dimensioning for Parallel Manipulators: Workspace, Dexterity, and Energy

In mechanism design and in the particular case of the parallel manipulator, most optimization problems involve simultaneously optimizing more than one objective function. In this paper, a method to identify Pareto-optimal solutions for the design of low-mobility parallel manipulators is presented. A 4-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is taken as a case study. The design goals used are workspace volume and manipulator dexterity based on a dispersion weighted Frobenius norm. In addition, an expression for energy per cycle has been defined for different types of trajectory to evaluate the power drive. Finally, the set of Pareto-optimal solutions of the design parameters are represented in the design parameter space.

Design of Limb of 2R2T 4-DoF Symmetrical Parallel Manipulators

A systematic methodology is presented for design of 2R2T 4-DoF symmetrical parallel manipulators, based on the screw theory. Through analyse the given constraints of the moving platform, using the screw theory and the reciprocal screw theory. According to the reciprocal product between kinetic screw and constraint screw in screw theory, this method firstly creates possible limb structures and then generates different models of mechanism. enumerate the limb twist system. Based on the limb twist system, design the feasible limb structures and the potentially parallel manipulators.

Multiobjective Optimum Design of a Symmetric Parallel Schönflies-Motion Generator

The multiobjective optimization of a four-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is the subject of this paper. First, the inverse positioning problem is discussed, along with its velocity analysis. The workspace is then analyzed, thereby deriving a closed-form expression of the workspace volume, which depends on the orientation of the moving platform. Next, the isotropic design of the manipulator is obtained. Then, the dexterity analysis of the manipulator is conducted, which is one objective of the optimum design of the manipulator, a second objective being a normalized workspace volume. Finally, the results of the optimization process are reported in terms of a set of Pareto-optimum pairs of the design parameters.

Kinematics of a partially decoupled 3R2T symmetrical parallel manipulator 3-RCRR

The 3R2T (three rotational and two independent translational degree of freedom (DoF)) symmetrical parallel manipulator may be adopted in bionics, for example, simulating the motion of a cervical spine based on their mobility property and performance close to isotropic limit. However, up to now, characteristics of this class of manipulators have not been well studied because of its short history. Hence, to study the feasibility of this class of manipulator for bionics, kinematics for 3-RCRR is analysed including position, singularity, velocity, and acceleration. Different from other 3R2T 5-DoF symmetrical parallel manipulators, the mobility of 3-RCRR is partially decoupled, which makes the realization of control system easier than in others.

Kinematics and Closed Optimal Design of a Kind of PRRRP Parallel Manipulator

This paper addresses optimal kinematic design of a PRRRP (P-prismatic joint, R-revolute joint) parallel manipulator that is horizontally actuated by linear actuators. Kinematically, the symmetrical PRRRP parallel manipulator has only one geometric parameter, i.e., the link length of each of the two legs. Here, we propose a design approach utilizing a performance chart and local performance specification. The key problem in the design of the manipulator is the determination of not the link length but the workspace that the manipulator can reach satisfying the design specification. Such a kind of workspace when the link length unit is defined as the basic good-condition workspace (GCW). For the manipulator studied here, the link length is actually the ratio of the desired task workspace to the basic GCW. This paper gives an effective method to obtain the basic GCW with respect to indices in closed forms. One of the advantages of the method is that the basic GCW is achieved by taking into account both the global and local indices.

Optimum design of the 5R symmetrical parallel manipulator with a surrounded and good-condition workspace

This paper concerns the optimum design issue of the 5R symmetrical parallel manipulator with a surrounded workspace. Generally, such a manipulator has a very large workspace. With different working modes, a manipulator will have different singular loci and workspaces. In this paper, the singularity and the usable workspace without singularity inside will be determined for the manipulator with a specified mode. The usable workspace can be used to define the global conditioning index (GCI). In order to obtain the optimum design of the manipulator, a non-dimensional design space is established. Because each of the non-dimensional manipulators in the established design space can represent the performances of all of its possible similarity manipulators, the design space is a very useful tool for guaranteeing a global comparative result. Within the design space, the singularity, usable workspace and control accuracy (evaluated using the GCI) are studied and the corresponding atlases are constructed. Based on the atlases, one can synthesize link lengths of the manipulator studied with respect to specified criteria. One example will be given to show how to use the atlases. In particular, an example will be presented of reaching the optimum dimensional result with respect to a desired practical workspace based on the optimum non-dimensional result identified from the atlases. For the reason that using the atlases presented in this paper a designer can obtain the optimum result with respect to any specification, the optimum design method proposed in this paper may be accepted by others.

Workspace of parallel manipulators with symmetric identical kinematic chains

In this paper, we propound an analogous symmetric theorem of workspace for spatial parallel manipulators with identical kinematic chains, and then present a strict mathematic proof by splitting the problem into planar symmetry, rotational axis symmetry and point symmetry (centrosymmetry). Examples demonstrate that this theorem can be utilized to investigate the geometry shapes of the workspace and to guide the conceptual design of spatial parallel manipulators, especially for those complicated spatial parallel manipulators with full degrees of freedom (DoF). The theorem offers a concrete safeguard for the workspace analysis of any symmetric spatial parallel manipulators.