Singularity-free Workspace Research Articles

Kinematic Analysis of a New 3-DOF Parallel Wrist-Gripper Assembly with a Large Singularity-Free Workspace

This paper introduces a novel dexterous 3-DOF parallel wrist-gripper assembly with a large singularity-free range of motion. It consists of a zero-torsion 2-DOF parallel wrist and a 1-DOF parallel gripper. The wrist produces a 2-DOF sphere-on-sphere pure rolling motion. This large singularity-free 2-DOF sphere-on-sphere pure rolling motion of the wrist allows for smooth and precise manipulation of objects in various orientations, making it suitable for applications such as assembly, pick-and-place, and inspection tasks. Using a geometrical approach, analytical solutions for the inverse and forward kinematics problems of the wrist and gripper are derived. From the inverse kinematic equations, the Jacobian matrices are derived and it is shown that the whole workspace is free of type I and type II singularities. It is shown that with a proper choice of design variables, a large singularity-free range of motion can be obtained. The absence of singularities in the whole workspace of the wrist-gripper assembly is an important feature that enhances its reliability. Finally, the correctness of the derived equations for the wrist inverse and forward kinematics are verified using MSC Adams. These results confirm the feasibility and effectiveness of the proposed parallel wrist-gripper assembly. Overall, the novel parallel wrist-gripper assembly presented in this paper demonstrates great potential for improving the efficiency and flexibility of robotic manipulators in a variety of industrial and research applications.

Mobility, Kinematic, Singularity, and Workspace Analysis of a Translational Parallel Manipulator with 2(RRPaRR)-PRRR Kinematic Chains

This article presents an asymmetric parallel manipulator with 2(RRPaRR)-PRRR kinematic chains. This manipulator aims to operate as a lower-mobility parallel manipulator with the pure translational motion of its platform. Therefore, a series of analyses are performed to fulfill this intention. First, the mobility analysis is performed by applying the Grübler-Kutzbach equation and the screw theory. Then, the kinematic, singularity, and workspace analysis are applied to analyze this PM. As a result, the application of the screw theory for the configuration of its kinematic chains shows its mobility in a pure translational motion in space. Then, this manipulator has a closed-form solution for its direct kinematic problem expressed in a quadratic equation. By applying singularity and workspace analysis via visualization, the singularity-free workspace along the z-axis of its workspace can be identified. This can later be used as a useful workspace. Overall, the presented manipulator can be applied to a translational parallel manipulator

Workspace, Singularity, and Dexterity Analyses of a Six-Degrees-of-Freedom SDelta Robot With an Orthogonal Base Platform

Abstract The SDelta is a three-limb, six-degrees-of-freedom parallel kinematics machine, a pertinent candidate for high-speed operations by virtue of its simple architecture. The original design of the SDelta includes a planar base and moving platforms. Here, we propose a novel architecture for an improved SDelta, the orthogonal SDelta (OSD), with a cube-shaped orthogonal base platform. Inverse and forward position models are reported, along with singularity and dexterity analyses. Moreover, design parameters and mechanical constraints leading to a singularity-free workspace are provided. An evaluation of the system translational workspace and orientational capability, upon consideration of volume and dexterity, is included. The SDelta as well as a generic 6SPS mechanism (C, P, and S denote, respectively, the cylindrical, prismatic, and spherical kinematic pairs, the actuated pair is represented underlined, as P) are designed with the same parameters, then the performance of the SDelta, the OSD, and the 6SPS mechanisms are being compared. The results show that the orientational capability of the OSD is better than those of the 6SPS and the SDelta. Furthermore, the OSD has an average condition number of 2.9 over its translational workspace and 1.69 over a predefined effective regular workspace, which make the OSD a good candidate for operations that need both a high orientational capability and high dexterity.

Instantaneous Kinematics and Free-from-Singularity Workspace of 3-XXRRU Parallel Manipulators

3-XXRRU parallel manipulators (PMs) constitute a family of six-degrees-of-freedom (DOF) PMs with three limbs of type XXRRU, where R and U stand for revolute pair and universal joint, respectively, and XX indicates any actuated two-DOF mechanism that moves the axis of the first R-pair. The members of this family share the fact that they all become particular 3-RRU structures when the actuators are locked. By exploiting this feature, the present paper proposes a general approach, which holds for all the members of this family, to analyze the instantaneous kinematics, workspace, and kinetostatic performances of any 3-XXRRU PM. The results of this study include the identification of singularity conditions without reference to a specific actuation system, the proposal of two specific dimensionless performance indices ranging from 0 to 1, the determination of the optimal actuation system, and the demonstration that 3-XXRRU PMs, when appropriately sized and actuated, possess a broad singularity-free workspace that is also fully isotropic. These findings hold significance in the context of the dimensional synthesis and control of 3-XXRRU PMs. Moreover, when combined with the closed-form solutions for their positional analysis, as demonstrated in a previous publication by the same authors, 3-XXRRU PMs emerge as intriguing alternatives to other six-DOF PMs. The efficacy of the proposed approach is further illustrated through a case study.

Design of the five-bar linkage with singularity-free workspace

AbstractThis paper shows the kinematic analysis and the synthesis of the five-bar linkage with symmetrical structure and singularity-free dexterous workspace. The type synthesis of the five-bar linkage shows that the number of symmetrical structures of five-bar linkage is limited to eight structures. This study deals with the forward and inverse kinematic analysis and synthesis of the five-bar structure 5-RRRRR. The synthesis equations allow the analytical computation of the link lengths of a symmetrical five-bar linkage using only revolute joints to avoid the singularities in an imposed dexterous workspace. A numerical example of the symmetrical five-bar linkage is analyzed and synthetized theoretically and characterized by computing the performance indices. The tests on an experimental model of the five-bar linkage 5-RRRRR confirm the singularity-free dexterous workspace.

Study on transmission angle and singularity in 5R planar mechanism

Transmission angle is one of the important design criteria to be considered for the effective force and motion transmission of a mechanism. Poor transmission angles are detrimental to the performance of a mechanism as they exaggerate the effect of friction and clearances. In addition, the torque required to overcome external load tends to increase and the required torque capacity of the drive increases unnecessarily. The singularity positions in a workspace are closely related to the transmission angle of the manipulator configuration. For achieving a large singularity-free area, the configuration dimension needs to be increased. Even though the objective is to design a compact five-bar planar mechanism, the link dimensions are likely to increase to some extent while achieving the desired transmission angles. This paper deals with estimating the singularity-free area of a five-bar mechanism by considering variations in transmission angles for different link lengths. The generalized methodology presented in this work demonstrates the estimation of singularity-free largest reachable area and link proportions at which intra-link transmission angles are confined. A dimensionless singularity-free workspace index is proposed to quantify performance at various transmission angles.

Mapping the Tilt and Torsion Angles for a 3-SPS-U Parallel Mechanism

This article presents the analysis of a parallel mechanism of type 3-SPS-U. The usual singularity approach is carried out with respect to the Euler angles of the universal joint. However, this approach is computationally expensive especially when stacked structures are analyzed. Thus, the positioning of the mobile platform for the mechanism is analyzed using the theory of Tilt and Torsion (T&T). The singularity-free workspace and the tilt limits of the mechanism are disclosed through this method. These workspaces can then be mapped to the Euler angles of the universal joint and the relation between the T&T space and the Euler space is demonstrated and validated in this study. Initially, simulations are performed using the results of singularity analysis to have a comparison between the T&T space and the Euler space. Experimental validation is then carried out on the prototype of the mechanism to perform a circular trajectory, in line with the simulations. The outcome of this study will be helpful for the integration of the mechanism for a piping inspection robot and also for the analysis of stacked architectures.

Dexterity distribution design for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition

This paper presents a dexterity distribution design method for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition (SWD). The requirement of attitude adjustment for platform is described by time-varying Euler angles, by which the structural prototyping of universal-prismatic-spherical + spherical (UPS + S) parallel robot body can be generated via mechanism concept design. According to Kutzbach-Grubler formula regarding degree of freedom (DOF), the forward kinematics model is built, meanwhile, the reachable posture workspace of the robot can be depicted in 3D space by exploiting tilt-and-torsion method. The Jacobian matrix is extracted to reckon dexterous performance of the mechanism, including condition number, minimum singular value, manipulability and comprehensive evaluation index. The singularity degree within the design domain, from singularity-free to fully singularity, is comparatively ranked in polar coordinates, which constitutes the essence of SWD, the performance spectrum corresponding to the structural parameters can hereby be acquired for larger workspace and smaller singularity. The impedance control errors with parameter perturbation further validate the consistency of the singularity-free attitude from the perspective of dynamics. The physical experiments are carried out to verify the outcomes by virtue of multi-axis pose sensor array. Hence the presented SWD method has important application prospects regarding DOF coupling, especially in medical rehabilitation, industrial robotics, aerospace manufacturing and so forth.

Analysis and Design of a Novel Compact Three-Degree-of-Freedom Parallel Robot

Abstract This paper introduces a novel compact three-degree-of-freedom (DOF) parallel robot that will be used as a leg of a 9-DOF kinematically redundant parallel robot. First, the kinematic model of the robot is established based on geometric constraint conditions. Then, the inverse and forward kinematic problems are solved. The inverse problem is straightforward, while the forward problem can be solved analytically by three different approaches. Afterward, a singularity analysis is presented based on the Jacobian matrices derived from the kinematic model. The mathematical conditions for singularities are obtained and their geometric interpretation is given. Finally, the workspace of the robot is analyzed and is shown to correspond to a portion of a torus. The analysis reveals that the robot can have a singularity-free workspace of significant size relative to its footprint provided that some simple limitations are introduced at the design stage.

Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for general configurations

Parallel mechanisms suffer from type II singularities which reduce their useful orientational workspace. Adding kinematic redundancy in parallel mechanisms enhances their orientational workspace by providing singularity avoidance capabilities. However, an increasing number of kinematically redundant degrees of freedom (DOFs) requires additional actuators and makes the redundancy resolution more complex. Moreover, examples in the literature exist where a minimal number of kinematically redundant DOFs was used to produce a singularity-free orientational workspace for planar mechanisms. In this work, the architecture of a kinematically redundant (6+2)-DOF parallel mechanism akin to the well-known Gough–Stewart platform is studied, and its singularity locus is derived. The results show that, while some singularities still remain in the useful workspace of the mechanism, they can be accurately localized with simple closed-form analytical expressions for trajectory planning purposes. Furthermore, the redundancy resolution may find itself easy to handle, since the avoidable singularities and mechanical interference can be mapped into the 2-D space of the redundant parameters. Finally, the proposed architecture is considered as a compromise between obtaining a singularity-free workspace and handling easily the redundancy resolution for the trajectory planning.

АНАЛИЗ ВЛИЯНИЯ СИНГУЛЯРНОСТЕЙ НА РЕШЕНИЕ ПРЯМОЙ ЗАДАЧИ КИНЕМАТИКИ И ГЕОМЕТРИЮ РАБОЧЕГО ПРОСТРАНСТВА ПЛАТФОРМЫ ГОФА-СТЮАРТА

One of the obligatory requirements for parallel mechanisms design is the exclusion from theworkspace of singularities in which the mechanism loses its controllability and malfunctions mayoccur. The analysis of the workspace of the mechanisms of a parallel structure is more complicatedthan that for the mechanisms of a serial structure, especially if the mechanism has more thanthree degrees of freedom. The article considers the problem of analyzing the influence of singularitieson the solution of the forward kinematics and the geometry of the workspace 3/6 of theGough-Stewart platform (commercial name - "Hexapod"). A numerical algorithm for solving theforward kinematics of platform has been developed. It is based on the direct use of the system ofequations of the platform's kinematic constraints. Approximation of the set of solutions to the systemof equations is based on deterministic methods of global optimization. An analysis of thechange in the number of forward kinematics near the zone of singularities is performed. The analysisconsists of two stages. The first stage consists in solving the forward kinematics for the positionand orientation of the platform, at which singularities arises. The second stage consists insolving the forward kinematics for the case of a singularity and the case near a singularity.As a result of solving the forward kinematics, a different number of forward kinematics solutionsfor different cases was revealed. An algorithm has been synthesized that makes it possible to determinea singularity-free workspace free for given ranges of change in the platform orientationangles specified by Euler angles. An analysis of the dependence of the change in the volume of theworkspace depending on the range of change in the angles of the platform orientation was carriedout. The algorithms are implemented programmatically in the C++ programming language.The modeling was performed using parallel computing and the implementation of the export ofthree-dimensional models of the positions of the platform and workspace to the universal format ofthree-dimensional models STL.

Singularity Analysis and Representation of 6DOF Parallel Robot Using Natural Coordinates

Singularity research is carried out. The problem, which is about six-dimensional parameters of position and orientation can not realize three-dimensional visualization for 6DOF parallel robot, has been solved. Firstly, according to the structural characteristics of the 6DOF parallel robot with the planar platform, the position and orientation of the mobile platform are described, respectively, and the six equations of forward kinematics are established by choosing the natural coordinates of three representative points as parameters. Then, the singularities of the 6DOF parallel robot with a planar platform are divided into input singularity and output singularity. Aiming at the output singularity, in combination with six constraint equations among the position vectors of three representative points, an analytical algorithm is proposed to express the coupling singularity of position and orientation and the analytical expression is derived. In further research, three kinds of output singularities are found, the spatial distribution of the output singular trajectory is determined, and a unified three-dimensional fully visualized description of six-dimensional coupling variables is realized for the first time. The problems of finding the singular orientation at a given position or the singular position at a given orientation are solved. The analysis of the singularity lays a solid foundation for the description of the three-dimensional complete visualization of a six-dimensional singularity-free workspace based on forward kinematics. What is more, it has great significance for both trajectory planning and control design of the parallel robot.

Kinematic design of a translational parallel mechanism based on sub-kinematic chain determined workspace superposition

This paper presents the kinematic design of a translational parallel mechanism (PM) named Vari-Orthoglide by means of the workspace superposition, according to the sub-kinematic chain (SKC) based PM composition principle. The main topological characteristics of the manipulator with two SKCs under study, such as the position and orientation (POC) characteristics, degree of freedom (DOF) and coupling degree are analyzed, which turns out that the coupling degree equals to 1, implying the partially decoupled motion. With the topological characteristics based kinematic modeling principle, a symbolic model of the kinematics is established to derive its symbolic direct and inverse kinematic solutions. Based upon the direct kinematic solution, the workspaces for the two SKCs can be efficiently found. Moreover, the singularity loci are identified for finding the singularity-free workspace, where a regular workspace is fitted as the task workspace as expected. The presented work shows an approach to design translational parallel mechanisms considering motion decoupling and regular workspace, applicable to other types of parallel mechanisms.

Kinematic Analysis and Optimal Design of a Novel Schönflies-Motion Parallel Manipulator With Rotational Pitch Motion for Assembly Operations

Abstract This paper presents a novel Schönflies-motion Parallel Manipulator with RotationalPitch motion (SPM-RP) based on a single-platform fully parallel mechanism. An analysis of the position, workspace, velocity, and singularity of the SPM-RP is carried out in detail, and a dimensionless Jacobian is proposed to evaluate the manipulability of the SPM-RP. The analysis shows that the SPM-RP is with position-decoupled kinematics, a large singularity-free workspace, and excellent manipulability. The SPM-RP is actuated by four parallel prismatic actuators, enabling the manipulator to provide the identical kinematic performance at all generic cross sections perpendicular to the prismatic joint axes within its workspace. This paper thus proposes a reduced design optimization formulation, where the traditional optimization over the entire workspace is reduced to the optimization on a representative workspace cross section of the SPM-RP. According to this approach, the design optimization of the SPM-RP is carried out by maximizing its manipulability over the total orientation workspace, which is crucial for precision assembly. Based on the achieved optimal design, an SPM-RP prototype is developed. The mobility, orientation capability, total orientation workspace, and repeatability of the optimal design are tested and verified by the developed SPM-RP prototype. Experiments show that the SPM-RP can achieve a large total orientation workspace with excellent precision performance.

Workspace Augmentation for the Large-Scale Spherical Honeycombs Perfusion Using a Novel 5DOF Reconfigurable Manipulator

Abstract The volume of workspace is a significant kinematic index of parallel manipulator in some applications of engineering. However, the workspace degradation of the manipulator in extreme position is a demanding issue, which results in a fact that such manipulators cannot satisfy the machining requirement of the maximum limit position for the large-scale complex structural components. In this paper, a novel five degrees-of-freedom (DOF) 5PRR+5PUS-PRPU parallel manipulator (PM) is presented. First, the mobility analysis for the proposed manipulator is carried out, and the inverse kinematics as well as the Jacobian matrix is developed. Then, the workspace of the 5PRR+5PUS-PRPU PM and the 5PUS-PRPU PM is analyzed to study the workspace augmentation of the proposed PM. The workspace comparisons of these two PMs prove that the proposed PM not only can realize the large movement of the moving platform along the z-axis, but also possess larger workspace than the 5PUS-PRPU PM when the moving platform has a large movement along the z-axis. Furthermore, the singularity analysis is also conducted to show the singularity-free workspace of the proposed PM. By the introduction of the reconfigurable 5PRR PM, the proposed manipulator effectively augments the reachable workspace of the moving platform along the z-axis and to some extent also solves the issue of workspace degradation of the PM along z-axis.

Efficient Singularity-Free Workspace Approximations Using Sum-of-Squares Programming

Abstract In this paper, we provide a general framework to determine inner and outer approximations to the singularity-free workspace of fully actuated robotic manipulators, subject to Type-I and Type-II singularities. This framework utilizes the sum-of-squares optimization technique, which is numerically implemented by semidefinite programming. In order to apply the sum-of-squares optimization technique, we convert the trigonometric functions in the kinematics of the manipulator to polynomial functions with an additional constraint. We define two quadratic forms, describing two ellipsoids, whose volumes are optimized to yield inner and outer approximations of the singularity-free workspace.

Design of a 3-DOF Parallel Manipulator to Compensate for Disturbances in Facade Cleaning

This paper proposes a three-degree-of-freedom manifold composed of three linear actuators. The proposed mechanism consists of a workspace suitable for facade cleaning and can compensate for the horizontal position from disturbances in a gondola-based exterior-wall cleaning. We design a cleaning manipulator that can ensure a constant cleaning area by compensating for the disturbance in each direction. The position, velocity kinematic, and Jacobian-based singularity analysis are presented, and kinematic variables are defined to extend a singularity-free workspace. In addition, optimization is performed based on an index that demonstrates the mechanical properties of the manipulator. The result shows how the manipulator compensates for the disturbances as well as the features of the optimization model. This study can be applied to robot manipulators for facade cleaning in the future.

A Systematic approach for designing a multi-function sit-to-stand mobility assistive device based on performance optimization

ABSTRACTRecently, the potential of assistive robots to enhance independence and quality of life for elderly and disabled has been given much attention. Designing a multi-function sit-to-stand assistive device is a challenging task due to the high payload and large workspace requirements. In this paper, a parallel manipulator-based assistive device is proposed to assist in various lower limb activities. The device is constructed based on a non-conventional structure of a 3- parallel manipulator, that provides partial kinematic decoupling between position and orientation and suitable singularity-free workspace as well as high rigidity and payload capability. Furthermore, dimensional synthesis based on maximizing the workspace index as well as the global force transmission and stiffness indices, is performed to optimize the device dimensions. A prototype of the device is manufactured based on the optimized dimensions. The ability to assist subjects with different stature heights to stand up in a natural manner is asserted by experiments conducted using the prototype.

Dexterous Workspace Optimization for a New Hybrid Parallel Robot Manipulator

In this paper, a new hybrid parallel robot (HPR) manipulator is introduced. First three kinematic limbs of six-legged general Stewart platform (6DOF GSP) manipulator are disconnected. Afterward, each passive universal joint of remaining three-legged parallel manipulator (three-UPS) is mounted at the center of each second passive revolute joint of RPR planar parallel manipulator (3DOF PPM) where underlined letters present active joints. Active actuators of PPM mounted between base platform of GSP and ground perform translations along x and y-axes, and rotation about z-axis. Remaining three limbs of GSP mechanism provide translation z-axis, and rotation about x- and y-axes only. Thus HPR can perform motion with full dimensions (translation and rotation about x-, y-, and z-axes). Optimizations are performed by using particle swarm optimization algorithm. Optimization results demonstrated that HPR provides better dexterity and singularity-free workspace characteristics than GSP.

Comparison of 3-[PP]S Parallel Manipulators based on their Singularity Free Orientation Workspace, Parasitic Motions and Complexity

The choice of a parallel manipulator for a particular application is a challenging task due to the existence of numerous designs that generate the same motion type. Hence, this paper attempts to compare a class of 3 degree-of-freedom parallel manipulators belonging to the 3-[PP]S family, for which each leg is confined to move in a plane with the first two joints generating a motion equivalent to two coplanar translations. Specifically, the 3-[PP]S parallel manipulators in which the planes are arranged in a Y-pattern are considered and are compared with respect to their singularity-free orientation workspace, parasitic motions within that workspace and complexity indices. Moreover, the comparison is done between the 3-[PP]S-Y family of manipulators for their different operation modes, with different actuation schemes and for different sets of design parameters. Two indices are used to quantify the singularity-free workspace and the parasitic motions of the manipulators at hand. Additionally, the non-dominated manipulator architectures with regard to their singularity-free regions and parasitic motions are highlighted thanks to a Pareto front. Finally, the Pareto-optimal solutions are ranked in ascending order of complexity.