Parallel manipulator kinematics learning using holographic neural network models

Type synthesis of multimode parallel manipulators (PMs) (also parallel manipulators with multiple operation modes) is an open issue in the research on reconfigurable mechanisms and robots. This paper deals with the type synthesis of 3-DOF (degree-of-freedom) parallel manipulators with both a planar operation mode and a spatial translational operation mode. The type synthesis of planar parallel manipulators, which refer to parallel manipulators in which the moving platform undergoes planar motion, is first dealt with using the virtual-chain approach. Types of planar parallel manipulators, including those involving Bennett compositional unit (CU), are obtained. Then, the types of 3-DOF parallel manipulators with both a planar operation mode and a translational operation mode are obtained. This paper focuses on 3-DOF parallel manipulators composed of only revolute joints. This work contributes to the type synthesis of parallel manipulators and can be extended to the type synthesis of other classes of multimode parallel manipulators.

In the traditional three DOFs (degrees of freedom) PMs (parallel manipulators), the terminal constraints are constraint forces and torques. A recent study showed that the terminal constraints of some three DOFs PMs are screw-type constraints. However, determining the mobility of this class of PMs remains challenging. In order to solve the above problems, this paper discusses the mobility of PMs having independent screw-type terminal constraints by introducing the principal screws. Firstly, taking a 3-CCR (C: cylindrical joint, R: revolute joint) PM as an example, the problem of identifying the mobility of PMs having screw-type constraints is proposed. Secondly, combined with the analytical expression of the terminal constraint and theory of quadratic curve decomposition, the mobility determination approach is given. Finally, a numerical example for solving the principal screws and determining the mobility of the 3-CCR PM is provided. Furthermore, the axodes of four poses with three helical DOFs and four poses with three rotational DOFs were plotted. The results show that there is a special phenomenon in which three rotational DOFs and three helical DOFs exist alternately in the workspace of this PM. This paper provides a method for directly identifying the independent helical DOFs in parallel manipulators and for studying the distribution of helical DOFs within the workspace.

This work presents a new systematic solution to identify the vehicle inertia parameters which are essential inputs for vehicle simulation and vehicle safety research. In conceptual design phase of this work, a virtual three Degree-of-Freedom (DoF) test bench/ parallel manipulator (PM) whose moving platform is used to clamp vehicle under test is developed. In order to realize the kinematic characteristics of the proposed PM, the kinematic analysis consists of inverse kinematic and singularity architecture is carried out. Aiming at obtaining all ten vehicle inertia parameters (i.e., mass, center of gravity and inertia tensor), the observation matrix for parameter identification is derived from the dynamic model of PM. To get the dynamic model, the Euler’s equation and Lagrange approach are applied to implement the dynamic analysis for PM’s moving platform and actuators, respectively. It is beneficial to reduce the complexity of dynamic model and load of numerical computation. In the following section, to minimize the sensitivity of parameter identification to measurement noise, an optimization process of searching for the optimal movement trajectory of PM is proposed. For this purpose, the parameterized finite-Fourier-series are used to definite the general movement trajectory of PM firstly. Subsequently, the parameters of general trajectory are optimized by employing a nonlinear iterative algorithm. Objective of this algorithm is to obtain the minimal condition number of observation matrix and meanwhile to ensure the PM still works in the achievable working space during the test. The results show that the vehicle inertial parameters can be effectively identified by executing the single optimal movement trajectory on the PM. It is expected that the proposed systematic solution could be an important approach to improve the identification efficiency and identification accuracy of vehicle inertial parameters.

The type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. This paper presents a systematic classification of a 3-RER PM based on the type/number of operation modes. Here, R and E denote revolute joint and planar joint, respectively. The 3-RER PM was proposed as a 4-degree-of-freedom (DOF) 3T1R PM in the literature. Using the proposed method, classification of a PM based on the type/number of operation modes can be carried out in four steps, including formulation of constraint equations of the PM, preliminary classification of the PM using Gröbner cover, operation mode analysis of all the types of PMs using primary decomposition of ideals, and identification of redundant types of PMs. The classification of the 3-RER PM shows that it has 13 types. Besides the two 4-DOF 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. Motion characteristics of the moving platform of 3-RER PMs are also identified using Euler parameter quaternions. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and provides a solid foundation for further research on the design and control of 3-RER PMs and other multi-mode (or reconfigurable) PMs.

Parallel manipulators (PMs) are often used as parallel kinematic machines (PKMs), which are more accurate and have more payload capacity compared to their serial counterparts. Spherical joints are frequently used in the construction of PKMs; however, spherical joints have a unique physical constraint, known as cone angle limit, around their axis of symmetry. The present work investigates the effect of changing the orientation of the spherical joint symmetry axis (SJSA) on the kinematic performance of PMs. Workspace index, global conditioning index, kinematic conditioning index and global stiffness index are chosen as performance indices. It is found that changing the orientation of SJSA has a remarkable impact on the kinematic performance of PMs. Also, it is shown that considering the cone angle limits considerably affect the kinematic performance of PMs. To demonstrate the results, two PMs, namely 3-PRS (P, R, and S denote prismatic, revolute, and spherical joints, respectively) and 3-RPS manipulators with spherical joints with adjustable axis of symmetry orientation, are used. The effect of changing SJSA orientation on various performance indices is carried out, and optimal orientation values are determined. Genetic algorithm (GA) optimization technique and traditional method are used. The results obtained using the two methods matched very well. It is found that orientation of the SJSA is one of the important PMs optimization parameters that should be considered during the design process.

Parallel manipulators have been used for a variety of applications, including the motion simulators and mechanism for precise machining. Since the ball screws used for linear motion of legs of the Stewart-Gough type parallel manipulator provide wider contact areas than revolute joints, parallel manipulators are usually more affected by frictional forces than serial manipulators. In this research, the method for detecting the frictional forces arising in the parallel manipulator using the gravitational force is proposed. First, the reference trajectories are computed from the dynamic model of the parallel manipulator assuming that it is subject to only the gravitational force without friction. When the parallel manipulator is controlled so that the platform follows the computed reference trajectory, this control force for each leg is equal to the friction force arising in each leg. It is shown that control performance can be improved when the friction compensation based on this information is added to the controller for position control of the moving plate of a parallel manipulator.

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.

The main objective of our work is to optimize the positional and orientation error of a platform using the direct geometric model of a parallel plane manipulator robot. It is well known that the main disadvantage of parallel manipulators is the existence of singularities within its workspace, the adaptive neuro-fuzzy solution is proposed in this study. Intermediate methods have been used to determine the optimal solution. The first method is a graphical method which determines all possible positions of the platform based on the intersection of circles. The second method is the polynomial method used to calculate the coordinates of the center of gravity and the orientation of the platform. Matlab programming simulation of these methods makes it possible to find all the solutions deduced from these methods. The analysis shows that the polynomial method is the one that provides the optimal solution.

This paper deals with the reconfiguration analysis of a 4-DOF (degrees-of-freedom) 3-RER parallel manipulator (PM) with equilateral triangular base and moving platform (ETBP), which is a special case of a 4-DOF PM in the literature. The 4-DOF 3-RER PM is composed of a base and a moving platform connected by three 3-RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. At first, a set of constraint equations of the 3-RER PM with ETBP is derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved in closed form. It is found that the 3-RER PM with ETBP has three 4-DOF operation modes if both the base and moving platform are identical or two 4-DOF operation modes if the base and moving platform are not identical. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the author of this paper. The transition configurations among different operation modes are also identified.

An integrated open-die forging centre can realize programmed incremental forging processes to improve safety and efficiency; the centre consists of a forging press and one or two heavy-duty manipulators. This paper focuses on the coordinated kinematic modelling of the integrated system. First a newly designed serial—parallel forging manipulator is presented and the closed-form inverse kinematic solution is derived based on homogeneous co-ordinate transformation. Then the deformation of the forged workpiece is investigated by the spread coefficient method of plastic deformation theory, and the relation between the motion of the holding end of the workpiece and the movement of the upper die is formulated. Finally, the coordinated kinematic modelling of the integrated system is established, where the press and the manipulator are coordinated in movement. Simulation of a typical open-die forging process shows that the gripper of the manipulator should have good compliance abilities in horizontal and vertical directions during forging; however, it should have high rotation stiffness with respect to the transverse axis. The automatic programmed forging plan and coordination control strategy can be pre-designed based on this model.

Analysis of a novel cylindrical 3-DoF parallel robot

A new 3T1R parallel manipulator (PM) 2PPaRR-2PPaRU with rotational pitch motion is proposed in this paper. In such a mechanism, there are four limbs connected to the moving platform (MP) through several revolute joints and universal joints, and all actuated joints are prismatic joints with an axis along a vertical direction. Mobility and motion characteristics are verified by constraint screw theory. The inverse kinematic solutions and the singularity configurations are derived through kinematic analysis. Next, the workspace analysis and the connection between [Formula: see text] and the volume of the reachable workspace are performed. The local motion/force transmission index is selected to evaluate the local transmission performance of 2PPaRR-2PPaRU PM. Finally, the global motion/force transmission index and the volume of reachable workspace are considered simultaneously to optimize the structural parameters. The 2PPaRR-2PPaRU PM with improved local transmission performance and reachable workspace has been achieved after optimization.

A parallel manipulator provides an alternative design to serial manipulators, and can be found in many applications such as mining machines (Arai et al., 1991). Through the design of active joints such that actuators are fixed to the manipulator base, the mass of moving components of the parallel manipulator is greatly reduced, and high speed and high acceleration performance may be achieved. Parallel manipulators, comprised of closed-loop chains due to multiple linkages of the parallel structure, also provide high mechanical rigidity, but adversely exhibit smaller workspace and associated singularities. Considerable research has focused on kinematic analysis and singularity characterization of these devices (Gosselin & Angeles, 1990, Merlet, 1996). Planar parallel manipulators typically consist of three closed chains and a moving platform. According to the arrangement of their joints in a chain, these mechanisms are classified as PRR, RRR etc. where P denotes a prismatic joint and R denotes a revolute joint respectively. An assembly industry, such as the electronic fabrication, demands high-speed, high acceleration placement manipulators, with corresponding lightweight linkages, hence these linkages deform under high inertia forces leading to unwanted vibrations. Moreover, such multiple flexible linkages of a parallel manipulator propagate their oscillatory motions to the moving platform where a working gripper is located. Therefore, such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. A number of approaches to develop the dynamic model of parallel manipulators with structural flexibility have been presented in the literature(Fattah et al., 1995, Toyama et al. 2001), but relatively few works related to vibration reduction of a parallel manipulator have been published. Kozak (Kozak et al., 2004) linearized the dynamic equations of a two-degree-of-freedom parallel manipulator locally, and applied an input shaping technique to reduce residual vibrations through modification of the reference command given to the system. Kang (Kang et al., 2002) modeled a planar parallel manipulator using the assumed modes method, and presented a two-time scale controller for linkage vibration attenuation of the planar parallel manipulator. Since both the input shaping technique and the two-time scale control scheme, applied to parallel manipulators,

Parallel robot inverse kinematics solution is relatively easier to obtain than forward kinematics forward, this paper assumes that the forward kinematics of six-DOF parallel robot is given then using the kinematics inverse solution to approximate the forward solution. To improve efficiency and stability of the approximation, an adaptive parameters differential evolution algorithm is proposed and applied to the forward kinematics problem. The experimental results show that the modified algorithm can gain the forward kinematics of parallel robot efficiently.

This paper presents the most important steps of the wrist rehabilitation robot design. In this work, kinematic synthesis problem of a 3-RRR spherical parallel manipulator is considered including a solution for forward and inverse kinematic problems. In order to maximize dexterity of the parallel manipulator over its workspace, its design is developed by finding optimal link shape parameters. The CAD design for the prototype is obtained based on this optimization.