General Parallel Manipulator Research Articles

Kinematics analysis of a novel hybrid manipulator for optomechanical modules assembly

A novel hybrid manipulator is proposed in this work, in order to assemble optomechanical modules in an inertial confinement fusion facility (SG-Ⅲ). Differ from general serial and parallel manipulators, both the inverse and forward kinematics problems of hybrid manipulators are difficult to be solved. Based on an analytic method, the position and orientation mapping functions between the optomechanical module and the parallel manipulators are established, and then the method of transformation matrix is employed to obtain the inverse kinematics solution. The forward kinematics of this hybrid manipulator is highly nonlinear and coupled, so a back propagation neural network using all class one network strategy is trained to approximate the mapping relation. Aiming to improve the accuracy, the network is split into two sub-networks corresponding to the natural property of the outputs. In the end, an improved back propagation neural network is proposed to optimize the network, results illustrate that the kinematic accuracy is increased significantly.

PhyNRnet: Physics-informed Newton-Raphson Network for Forward Kinematics Solution of Parallel Manipulators

Abstract Despite significant performance advantages, the intractable forward kinematics have always restricted the application of parallel manipulators to small posture spaces. Traditional analytical method and Newton-Raphson method usually cannot solve this problem well due to lack of generality or latent divergence. To address this issue, this study employs recent advances in deep learning to propose a novel physics-informed Newton-Raphson network (PhyNRnet) to rapidly and accurately solve this forward kinematics problem for general parallel manipulators. The main strategy of PhyNRnet is to combine the Newton-Raphson method with the neural network, which helps to significantly improve the accuracy and convergence speed of the model. In addition, to facilitate the network optimization, semi-autoregression, hard imposition of initial/boundary conditions (I/BCs), batch normalization, etc. are developed and applied in PhyNRnet. Unlike previous data-driven paradigms, PhyNRnet adopts the physics-informed loss functions to guide the network optimization, which gives the model clear physical meaning and helps improve generalization ability. Finally, the performance of PhyNRnet is verified by three parallel manipulator paradigms with large postures, where the Newton-Raphson method has generally diverged. Besides, the efficiency analysis shows that PhyNRnet consumes only a small amount of time at each time step, which meets the real-time requirements.

A Conceptual and Straightforward Approach for Solving the Closed-form Direct Kinematics of a General Coplanar 6-PUS Parallel Manipulator

A Conceptual and Straightforward Approach for Solving the Closed-form Direct Kinematics of a General Coplanar 6-PUS Parallel Manipulator

A novel 6 DOFs generalized parallel manipulator design and analysis based on humanoid leg

In this paper, a 6 degrees of freedom (DOFs) generalized parallel manipulator is presented which can be used as a humanoid leg. Based on the Number Synthesis and Graph Synthesis method, all the possible contracted graphs of the 6-DOFs leg are provided. Then, a novel method named as Node Response Method (NRM) is presented to identify the isomorphism of contracted graphs. In order to obtain the optimal manipulator, the Lie group is used to analyze all limbs. Furthermore, a terrain adaptive index named as Global Maximum Stride Distance Ratio (GMSDR) is established, which is used to assess the performance of a biped robot in different terrains. The DOF of proposed manipulator is verified by translating into a two-layer and two-loop (TL-TL) topological structure. Afterwards, the kinematics and the Jacobian matrix of the manipulator are calculated. Moreover, the performance indexes of the manipulator are analyzed. In order to obtain an optimal kinematics performance, the structural parameters are optimized using genetic algorithm. Finally, two basic gaits are proposed for a biped robot which consists of two manipulators and a simulation is carried out.

Full dynamic model of 3-UPU translational parallel manipulator for model-based control schemes

AbstractOptimal mechanical design, model-based control, and robot dynamic calibration mainly rely on the analytical formulation of robot dynamics. In this paper, the kinematics equations of a general 3-UPU translational parallel manipulator (TPM) are derived, and then, by using the principle of the virtual work theorem, the full implicit dynamic model is derived. Furthermore, by making some modifications, the explicit dynamic formulation of the robot is attained, which is the basis of a wide range of advanced model-based controllers. To validate the proposed formulation, a prototype of the 3-UPU TPM is modeled in MSC-ADAMS® software, and the results of the dynamic formulation are validated using this model. The results show the high accuracy of the proposed dynamic formulation presented in this article.

Kinematic Analysis and Optimization of a Novel Single-Loop Generalized Parallel Manipulator for Scara Motion

Kinematic Analysis and Optimization of a Novel Single-Loop Generalized Parallel Manipulator for Scara Motion

Kinematic Analysis of a Novel Single-Loop Generalized Parallel Manipulator with a Compact Traveling Platform for Scara Motion

Kinematic Analysis of a Novel Single-Loop Generalized Parallel Manipulator with a Compact Traveling Platform for Scara Motion

Kinematics of a 6-DOF parallel manipulator with two limbs actuated by spherical motion generators

Inspired by dual-arm-like manipulation, a novel 6-DOF parallel manipulator with two spherical-universal-revolute limbs is proposed. Compared with general 6-DOF parallel manipulators with six limbs, this new manipulator actuated by spherical motion generators has only two limbs, which brings advantages such as fewer active limbs for avoiding interference, larger reachable and orientational workspace for complex operating, more actuators integrated in active modules for decreasing installation errors and increasing compactness. In this paper, the kinematics of this novel parallel manipulator is solved and illustrated, covering its inverse and forward position analysis, workspace and singularities. The kinematic study reveals interesting features of this manipulator such as multiple working and assembly modes, small footprint and large workspace volume with high dexterity. Numerical examples of kinematic analysis are included. Practical application of the new manipulator is illustrated.

Kinestatic Analysis of General Parallel Manipulators

Robotic mechanisms in general can be of either serial-chain, parallel-chain, or hybrid (a combination of both parallel and serial chains) geometry. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when it is considered in the general context. In this article, we present a general procedure for systematic formulation and characterization of the instantaneous kinematics for a robotic mechanism with a general parallel-chain geometry. A kinestatic approach based on screw system theory is adopted in this treatment. The resulting equation is a compact Jacobian matrix of the system which includes attributes from not only the active joints but also the passive constraints. An example has been provided to demonstrate the methodology as well as its theoretical feasibility.

A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators

This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.

Parametric design and multi-objective optimization of a general 6-PUS parallel manipulator

Parallel robots usage as motion simulators is increasing. Among them, the Stewart robot is most commonly used. However, a properly selected 6-PUS architecture seems to potentially offer certain advantages over the popular 6-UPS structure. To prove this hypothesis, the FUM-Stewart-M450 robot is selected as a case study in this study. The parameters representing overall robot size and desired workspace are considered to be the same in both the 6-UPS and 6-PUS robots for a fair comparison. To fully define the 6-PUS robot, three performance indices, dexterity, kinetic energy and a new modified workspace index are used for optimal determination of the remaining parameters. The proposed workspace index is specifically designed for motion simulators. It not only considers the robot workspace in all 6 degrees-of-freedom but also takes into account the main feature of motion simulators motion cues, their return to home for each subsequent motion. The Pareto front is used to compare various 6-PUS designs with the FUM-Stewart-M450. The results indicate that among the optimized robots, there exists an architecture that significantly lowers maximum actuator's static and dynamic forces. This paper offers a general outline for optimization and comparison of various robot structures having combined rotational-translational motion.

A novel class of generalized parallel manipulators with high rotational capability

A conventional parallel manipulator is characterized by connecting one moving platform with two or more serial kinematic limbs. Since each limb is independently supporting one moving platform, the moving platform must be a rigid body with several kinematic pairs fixed on it. However, for generalized parallel manipulators with articulated moving platforms, the moving platforms are not limited to rigid bodies but including serial kinematic chains or internal kinematic joints. The introduction of articulated moving platforms allows for improving the kinematic performance of generalized parallel manipulators, especially for rotational capability. On account of the structural characteristics of the moving platforms, it also poses a significant challenge in the construction of the structures of manipulators. This research raises a new method for the type synthesis of generalized parallel manipulators with novel articulated moving platforms. The proposed method introduces a striking shortcut for the limb structure analysis of mechanisms with high rotational capability. In this paper, a class of generalized parallel manipulator with different degrees of freedom from 3 to 6 are constructed by using the constraint synthesis method, and several examples are provided to demonstrate the feasibility of the advocated method. At last, the 3T3R generalized parallel manipulator is taken as an example to analyze the inverse kinematics, and the evaluation of the workspace is conducted to verify the rotational capacity.

Unified motion reliability analysis and comparison study of planar parallel manipulators with interval joint clearance variables

Motion reliability is a significant performance index for manipulators with uncertainties. This paper presents a unified motion reliability analysis method for general planar parallel manipulators (PPMs) with interval clearance variables of revolute and prismatic joints. The uncertainties of manufacturing and inputs are also considered and assumed to follow normal distributions. Two typical types of PPMs, 3RRR PPM and 3PRR PPM, are analyzed as examples to demonstrate the effectiveness of the method. For the purpose of a relatively fair comparison, the two PPMs are designed to have the same sizes of base platforms and moving platforms by using a traditional kinematic optimization based on the global conditioning index (GCI). Then, the comparison studies of the two PPMs are made with respect to performance indices of GCI, LCI (local conditioning index) and motion reliability. Furthermore, the index comparison between LCI and motion reliability is also carried out in detail through the two PPMs. The numerical analysis results indicate that: (i) the presented method could achieve a higher confidence estimate compared with the traditional probability method; (ii) the 3PRR PPM exhibits better motion reliability performance than the 3RRR PPM at the same uncertainty levels; and (iii) the traditional optimization based on the GCI cannot guarantee the good motion reliability performance of the PPM. This study provides support for the design and control of PPMs in terms of accuracy and motion reliability.

Workspace characterization and kinematic analysis of general spherical parallel manipulators revisited via graphical based approaches

This paper revisits some fundamental issues in kinematic analysis of spherical parallel robotic manipulators (SPRMs), such as the orientation capacities of the mobile platform (MPF), and assembly modes determination. The orientation capacities are analyzed by using several types of workspaces: total orientation workspace, full-spin orientation workspace, and constant-spin orientation workspace. The adopted representation of the MPF orientation brings up-to-date the use of the spherical coordinate system, which we find more appropriate when Euler angle orientation parameters are used. This representation is applied to each limb, considered independent from the rest of the mechanism and having the mobile platform as end-effector. The 3D orientation space reached by each limb, which is called also vertex space, is represented as a 3D solid volume. Thereafter, the operational space of the SPRM is directly determined by the Boolean intersection of the previously obtained volumes. Moreover, by fixing the joint space variables, the domain reached by each limb in the operational space is a surface. The Boolean intersection of the obtained surfaces is nothing but the set of points corresponding to the solutions of the forward kinematic problem. These operations are implemented in CAD software and the proposed approaches have been validated successfully by using several examples of application for both workspace determination and representation and FKP resolution.

Kinematic design and novel mobility analysis of a new 3D pantograph decoupled manipulator

A new decoupled 3D translational pantograph manipulator with symmetrical design is proposed. Since its three linear actuators are placed on/near the base, it possesses, to some extent, the advantages of parallel manipulators such as high speed, high stiffness and high accuracy. Since its structure is close to that of serial manipulators, its workspace to size ratio is high, comparable to that of serial manipulators. Moreover, the end-effector of the proposed manipulator has decoupled translation motions in three perpendicular directions with fixed orientation. Also, the manipulator has a linear input/output relationship for the positioning problem. Other possible architectures for the proposed manipulator are presented where the manipulator can have 4, 5 or 6 DOFs. The unconventional interconnected structure of the proposed manipulator does not allow the use of known mobility analysis methods. So, a novel method based on sketching the 3D velocity diagram is developed to derive the full-cycle mobility for general (serial, parallel or interconnected) manipulators. The kinematics, workspace, singularity and stiffness of the proposed manipulator are studied. The results show that the proposed manipulator outperforms the known translational decoupled Pantopteron manipulator regarding the workspace to size ratio. The proposed manipulator can also achieve configuration-independent and near-isotropic behaviors.

Design optimization of 3PRS parallel manipulator using global performance indices

This paper presents an optimal kinetostatic design method for a general 3PRS (Prismatic-revolute-spherical) spatial parallel manipulator by formulating a multi-objective optimization problem considering the performance indices are as the objective functions. Three performance criteria—Global conditioning index (GCI), Global stiffness index (GSI) and workspace volume-were formulated and the effect of actuator layout angle on the performance indices was studied. A multi-objective evolutionary algorithm based on the Control elitist non-dominated sorting genetic algorithm (CENSGA) was adopted to find the final approximation set. The optimal geometric parameters that yield minimal compliance with larger workspace volume and improved dexterity are suggested for a general 3PRS parallel manipulator. For the optimal design, it is shown that global isotropy and global stiffness of the platform is improved at the cost of workspace reduction.

Optimization design of general triglide parallel manipulators

Optimization design of parallel manipulators has attracted much interest from researchers in recent years. The reported methodologies attempted to achieve optimal design of parallel manipulators considering several properties, such as dexterity, stiffness, and space utilization, which are important parameters to be considered. However, stiffness analysis considered by many researchers generally ignores the deformation of the mobile platform. For space utilization, there is no reported method to consider the variation in the physical size caused by different postures of the manipulator. Additionally, although optimization of a linear delta and an orthoglide has been presented by several researchers, optimization of a general triglide has not been reported. In order to address these issues, this paper presents a multi-objective optimization addressing dexterity, stiffness, and space utilization of a general triglide. Its stiffness matrix is obtained considering the deformation of mobile platform, limbs, and actuators. A novel stiffness index is used to evaluate its stiffness property considering external wrench applied on the manipulator. The physical size of the triglide is represented using both a constant size and a variable size. Comparing with a reported optimization methodology, it is proven that the proposed method is capable of providing optimal solutions with better properties.

Atlas based kinematic optimum design of the Stewart parallel manipulator

Optimum design is a key approach to make full use of potential advantages of a parallel manipulator. The optimum design of multi-parameter parallel manipulators(more than three design parameters), such as Stewart manipulator, relies on analysis based and algorithm based optimum design methods, which fall to be accurate or intuitive. To solve this problem and achieve both accurate and intuition, atlas based optimum design of a general Stewart parallel manipulator is established, with rational selection of design parameters. Based on the defined spherical usable workspace(SUW), primary kinematic performance indices of the Stewart manipulator, involving workspace and condition number are introduced and analyzed. Then, corresponding performance atlases are drawn with the established non-dimensional design space, and impact of joint distribution angles on the manipulator performance is analyzed and illustrated. At last, an example on atlas based optimum design of the Stewart manipulator is accomplished to illustrate the optimum design process, considering the end-effector posture. Deduced atlases can be flexibly applied to both quantitative and qualitative analysis to get the desired optimal design for the Stewart manipulator with respect to related performance requirements. Besides, the established optimum design method can be further applied to other multi-parameter parallel manipulators.

Enhancing the useful workspace of a reconfigurable parallel manipulator by grasp point optimization

Reconfigurable parallel manipulators combine the properties of parallel manipulators with high flexibility. However, the workspace of parallel manipulators is, compared to serial manipulators, relatively small and hence the optimization of the useful workspace is an important design factor. Different efficient algorithms for calculating the workspace for parallel manipulators have been developed, but they need to be adapted to reconfigurable systems with additional parameters. These variables for those systems are the parameters of the reconfiguration, e.g. the grasping points. This paper presents a method to obtain the grasping point combinations of a parallel reconfigurable manipulator that leads to a useful workspace containing the largest geometric object. The largest geometric object inside the useful workspace describes its regularity and represents a useful evaluation criterion. The method is introduced for a general reconfigurable parallel manipulator and then studied for the particular case of the PARAGRIP reconfigurable parallel manipulator. The workspace is obtained by applying a combined geometrical and discretization method. To reduce the possible grasping point combinations and thereby reduce computational cost, we apply the special requirements that the grasping point combinations must fulfil. By solving the inverse kinematic problem for each combination the useful workspace is calculated. HighlightsWe present a method for parallel reconfigurable manipulators.We get the grasping point combinations with the biggest free-singularity workspace.We obtain the combinations that lead to the biggest sphere in the useful workspace.We introduce the method for a general case.We focus on the parallel reconfigurable manipulator PARAGRIP case.

The forward kinematics of the 6-6 parallel manipulator using an evolutionary algorithm based on generalized generation gap with parent-centric crossover

SUMMARYIn this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.