Spherical Parallel Manipulator Research Articles

A 3UPS/S Spherical Parallel Manipulator Designed for Robot-Assisted Hand Rehabilitation after Stroke

Hand dysfunction is a common symptom in stroke patients. This paper presents a robotic device which assists the rehabilitation process in order to reduce the need of physical therapy, i.e., a 3UPS/S parallel robotic device is employed for repetitive robot-assisted rehabilitation. Euler angle representation was used to solve the robot’s inverse kinematics. The robot’s joint space and rotational workspace were determined for two scenarios. In the first scenario, the workspace was obtained considering the actuator’s stroke limitations, while in the second scenario, the workspace was determined by adding a second condition, i.e., the range of motion of the spherical joints. Singularity analysis was performed using the geometric algebra approach. The robot was manufactured using additive manufacturing technology. The solution of the inverse kinematic problem was employed to control the robot. The robot can perform a full range of motion during wrist ulnar deviation and radial deviation motions, with the exception of limited wrist flexion and extension motions. The robot has singular configurations within its workspace. Although the spherical joints have roles in reducing the workspace, the primary causes are actuator selection, radii of the base and moving platforms, and the length of the central leg. These factors can be considered to improve the workspace. Singularity can be avoided by carefully selecting the rotation of the moving platform about the Z-axis and avoiding same leg lengths.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Modeling and optimization of a novel multi-DOF electromagnetic driven spherical motion generator

This paper introduces a new spherical motion generator and presents a method for modeling its magnetic field and analyzing its moments. The generator employs an electromagnetic drive of a spherical motor as its driving method and utilizes a spherical parallel manipulator to execute the spherical motion. The combination of these two technologies offers several advantages, including a large workspace and high motion accuracy. The equivalent magnetizing current method is used in the magnetic field modeling and the average air-gap flux density is optimized to achieve a better magnetic field distribution, and the accuracy of the analytical model is verified by finite element simulations and experiments.

Design, Analysis and Implementation of a 3-DOF Spherical Parallel Manipulator

Design, Analysis and Implementation of a 3-DOF Spherical Parallel Manipulator

A design of 2-DoFs spherical parallel manipulator with adjustable workspace

Spherical parallel manipulators (SPMs) have promising industrial applications due to their strong mechanical performance. However, they face challenges such as singularity avoidance, tight tolerance manufacturing requirements, and the need for versatile and dexterous end-effector functionalities. Additionally, SPMs lack customizability due to singularity and collision issues. This work introduces a novel design principle that addresses these challenges by benchmarking two analytical methods: structural synthesis using screw theory and dimensional synthesis using dimensionless parameters. A proof of concept of a 2-DoF SPM that can operate within a cylindrical constraint and realize a full workspace without collision is presented. This design allows for adjustable reachable workspace at the end-effector, despite significant geometric constraints. These findings on mechanical design solutions provide customizability for SPMs, and a 3D model with an aspect ratio of 1/12 is presented and discussed for potential practical applications. Overall, it is identified that both a simulation using Recurdyn and inverse kinematic model show the desired movements at the moving platform with the maximum error of 0.0013°.

On the Certification of the Kinematics of 3-DOF Spherical Parallel Manipulators

This paper aims to study a specific kind of parallel robot: Spherical Parallel Manipulators (SPM) that are capable of unlimited rolling. A focus is made on the kinematics of such mechanisms, especially taking into account uncertainties (e.g. on conception & fabrication parameters, measures) and their propagations. Such considerations are crucial if we want to control our robot correctly without any undesirable behavior in its workspace (e.g. effects of singularities). In this paper, we will consider two different approaches to study the kinematics and the singularities of the robot of interest: symbolic and semi-numerical. By doing so, we can compute a singularity-free zone in the work- and joint spaces, considering given uncertainties on the parameters. In this zone, we can use any control law to inertially stabilize the upper platform of the robot.

Dexterity, Workspace and Performance Analysis of the Conceptual Design of a Novel Three-legged, Redundant, Lightweight, Compliant, Serial-parallel Robot

In this article, the mechanical design and analysis of a novel three-legged, agile robot with passively compliant 4-degrees-of-freedom legs, comprising a hybrid topology of serial, planar and spherical parallel structures, is presented. The design aims to combine the established principle of the Spring Loaded Inverted Pendulum model for energy efficient locomotion with the accuracy and strength of parallel mechanisms for manipulation tasks. The study involves several kinematics and Jacobian based analyses that specifically evaluate the application of a non-overconstrained spherical parallel manipulator as a robot hip joint, decoupling impact forces and actuation torques, suitable for the requirements of legged locomotion. The dexterity is investigated with respect to joint limits and workspace boundary contours, showing that the mechanism stays well conditioned and allows for a sufficient range of motion. Based on the functional redundancy of the constrained serial-parallel architecture it is furthermore revealed that the robot allows for the exploitation of optimal leg postures, resulting in the possible optimization of actuator load distribution and accuracy improvements. Consequently, the workspace of the robot torso as additional end-effector is investigated for the possible application of object manipulation tasks. Results reveal the existence of a sufficient volume applicable for spatial motion of the torso in the statically stable tripodal posture. In addition, a critical load estimation is derived, which yields a posture dependent performance index that evaluates the risks of overload situations for the individual actuators.

Enhancing Kinematic Calibration Accuracy for Parallel Manipulators Based on Truncated Total Least-Square Regularization

Abstract This article proposes a novel kinematic calibration approach to address the ill-conditioned identification matrix problem and enhance the accuracy of parallel manipulators (PMs). The kinematic calibration approach applies the truncated total least-square (T-TLS) regularization method to the inverse kinematic calibration of PMs and does not have the unit inconsistency issue and configuration selection issue. The performance of the T-TLS method in the inverse kinematic calibration of PMs that have the ill-conditioned identification matrix problem is compared to that of classical regularization methods, including the truncated singular value decomposition (TSVD) method and Tikhonov method, in simulations. Then, the kinematic calibration approach is applied to a 3-PSS/S spherical PM prototype in the real world. For the 3-PSS/S spherical PM prototype, the kinematic calibration approach can reduce the absolute angular errors of the end-effector from over 1.0 deg before calibration to less than 0.1 deg after calibration.

Development of a novel hybrid haptic (nHH) device with a remote center of rotation dedicated to laparoscopic surgery

AbstractThis paper focuses on developing a novel hybrid-haptic (nHH) device with a remote center of rotation with 4 DOFs (degrees of freedom) intendant to be used as a haptic device. The new architecture is composed of two chains handling each one a part of the motions. It has the advantages of a parallel robot as high stiffness and accuracy, and the large workspace of the serial robots. The optimal synthesis of the nHH was performed using real-coded genetic algorithms. The optimization criteria and constraints were established and successively formulated and solved using a mono-objective function. A validation and comparison study were performed between the spherical parallel manipulator and the nHH. The obtained results are promising since the nHH is compared to other similar task devices, such as spherical parallel manipulator, and presents a suitable kinematic performance with a task workspace free singularity inside.

Comparative Analysis of Stiffness in Redundant Co-axial Spherical Parallel Manipulator Using Matrix Structural Analysis and VJM Method

Comparative Analysis of Stiffness in Redundant Co-axial Spherical Parallel Manipulator Using Matrix Structural Analysis and VJM Method

Designing and controlling a self-balancing platform mechanism based on 3-RCC spherical parallel manipulator

Motion control platforms have various applications in the manufacturing and automation industries. Different literature provides multiple issues related to the kinematics and dynamics of self-guided robots for transportation regarding platform balancing. Self-balancing platforms are utilized in many deliveries, stabilization, and transportation systems, and they are especially well suited for outdoor activities when the ground surface is not flat or structured. This paper describes developing a control technique for a self-balancing platform using the 3-RCC spherical parallel manipulator. This mechanism was designed to support an AGV (Automated Guided Vehicle) for transporting and lifting heavy weights for industrial applications. The AGV carries a robotic arm on top for different tasks. When the AGV encounters a steep slope or a rough surface, the AGV tilts, and the robotic arm’s performance is significantly affected. So, this study gives a solution to avoid these circumstances with a novel approach for the platform’s self-balancing mechanism consisting of a 3-RCC spherical parallel manipulator. Real-time stabilization and kinematics analysis methods are used to achieve the self-balancing system of the platform. When both methods are observed through different tilting angles for automation stability, Kinematic analysis performs more efficiently with less time duration when compared with the real-time stabilization method.

Development of a spherical parallel manipulator for brain surgery applications: preliminary study on the dynamic analysis and verification

AbstractThis study focuses on development, task planning, and dynamic analysis of a previously proposed spherical parallel robot manipulator that is conceptually enhanced to adapt various brain surgery scenarios. Conceptual design of the proposed manipulator was briefly introduced and explained. In order to simulate one of the possible surgery scenarios, a case study of craniotomy was designed along with its trajectory planning. Dynamic analysis of proposed manipulator was performed by Lagrange method, and required actuator torque values were calculated for the desired trajectory. At the end of the study, hardware verification was carried out on the manufactured prototype of the system by comparing both calculated/acquired torque values and desired/actual trajectories. Promising verification results in terms of system dynamics and trajectory execution were introduced.

Topological Analysis of a Novel Compact Omnidirectional Three-Legged Robot with Parallel Hip Structures Regarding Locomotion Capability and Load Distribution

In this study, a novel design for a compact, lightweight, agile, omnidirectional three-legged robot involving legs with four degrees of freedom, utilizing an spherical parallel mechanism with an additional non-redundant central support joint for the robot hip structure is proposed. The general design and conceptual ideas for the robot are presented, targeting a close match of the well-known SLIP-model. CAD models, 3d-printed prototypes, and proof-of-concept multi-body simulations are shown, investigating the feasibility to employ a geometrically dense spherical parallel manipulator with completely spherically shaped shell-type parts for the highly force-loaded application in the legged robot hip mechanism. Furthermore, in this study, an analytic expression is derived, yielding the calculation of stress forces acting inside the linkage structures, by directly constructing the manipulator hip Jacobian inside the force domain.

Infinite rotational motion generation and analysis of a spherical parallel manipulator with coaxial input axes

This paper presents a novel framework for the analysis of a 3-RRR spherical parallel manipulator with coaxial input axes (coaxial SPM) with the focus on its infinite rotational motion capabilities and its effects on the manipulator’s characteristics. The framework consists of three phases. At first, an approach for obtaining unique solutions of forward and inverse kinematics problems is introduced for setting up univocal relation between coaxial SPM’s input joint positions and orientation of its end-effector. At the second phase, a method for generating infinite rotational motions of an end-effector is formulated. The third phase outlines numerical computation procedures of the coaxial SPM’s workspaces in the joint and Cartesian spaces, excluding singularity configurations and mechanical collisions of SPM’s links during infinite rotational motion. A 3D design model and an experimental prototype of the coaxial SPM is presented and utilized for numerical analysis and experimental verification of the presented framework supplemented by an accompanying video demonstration.

Torque Reduction of a Reconfigurable Spherical Parallel Mechanism Based on Craniotomy Experimental Data

This paper deals with a robotic manipulator dedicated to craniotomy with a remote center of motion based on a Spherical Parallel Manipulator (SPM) architecture. The SPM is proposed to handle the drilling tool through the requested craniotomy Degrees of Freedom (DoF) with two rotations. The proposed architecture allows one degree of redundancy according to the total DoF. Thus, a first contribution of this work focuses on the experimental analysis of craniotomy surgery tasks. Secondly, its behavior is improved, taking advantage of the redundancy of the SPM using the spinning motion as a reconfiguration variable. The spinning angle modulation allows the reconfigurable manipulator to minimize its motor torques. A series of motion capture and force experimentations is performed for the analysis of the kinematic and force interaction characterizing Burr hole craniotomy procedures. Experimentations were carried out by a neurosurgeon on a human cadaver, ensuring highly realistic conditions.

Task-based torque minimization of a 3-PṞR spherical parallel manipulator

AbstractA comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

Singularity and branch identification of a 2 degree-of-freedom (DOF) seven-bar spherical parallel manipulator

Abstract. Spherical parallel manipulators (SPMs) have a great potential for industrial applications of robot wrists, camera-orientating devices, and even sensors because of their special structure. However, increasing with the number of links, the kinematics analysis of the complex SPMs is formidable. The main contribution of this paper is to present a kind of 2 degree-of-freedom (DOF) seven-bar SPM containing two five-bar spherical loops, which has the advantages of high reaction speed, accuracy rating, and rigidity. And based on the unusual actuated choices and symmetrical loop structure, an approach is provided to identify singularities and branches of this kind of 2 DOF seven-bar SPM according to three following steps. Firstly, loop equations of the two five-bar spherical loops, which include all the kinematic characteristics of this SPM, are established with joint rotation and side rotation. Secondly, branch graphs are obtained by Maple based on the discriminants of loop equations and the concept of joint rotation space (JRS). Then, singularities are directly determined by the singular boundaries of the branch graphs, and branches are easily identified by the overlapping areas of JRS of two five-bar spherical loops. Finally, this paper distinguishes two types of branches of this SPM according to whether branch points exist to decouple the kinematics, which can be used for different performance applications. The proposed method is visual and offers geometric insights into understanding the formation of mobility using branch graphs. At the end of this paper, two examples are employed to illustrate the proposed method.

Forward Kinematic Model Resolution of a Special Spherical Parallel Manipulator: Comparison and Real-Time Validation

This paper deals with a special architecture of Spherical Parallel Manipulators (SPMs) designed to be a haptic device for a medical tele-operation system. This architecture is obtained by replacing the kinematic of one leg of a classical 3-RRR SPM (R for revolute joint). The Forward Kinematic Model (FKM) is particularly addressed to allow the new master device to control the motion of a slave surgical robot. For this purpose, three methods are presented to solve the FKM and compared based on the criterion of time consuming and accuracy. For each method, namely, classic FKM, Improved method and serial FKM, the resolution procedure is detailed and the experimental validation is presented. After comparison, the serial approach involving the use of three sensors located on one leg of the master device is revealed as the most suitable. Experimental validation of the real-time motion control is successfully performed using the serial FKM.

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

This paper introduces a novel three degree-of-freedom spherical parallel manipulator with 3-PRR topology, where P and R denote a curved prismatic joint and a revolute joint, respectively. The first revolute joint of each PRR leg is actuated via a double Rzeppa-type driveshaft, and hence underlined. The manipulator has at most eight working modes and eight assembly modes. However, only one working mode and one assembly mode of the manipulator are acceptable during its motion which can be easily identified. Singularity and kinematic dexterity analyses reveal that the proposed 3-PRR spherical parallel manipulator has no forward kinematic singularity for a wide range of rotation of the moving platform around its central axis. An optimal design of the manipulator is also presented having a workspace with good kinematic dexterity.

Beyin Cerrahisi için bir Robot Manipülatör Tasarımının Geliştirilmesi

Nowadays, most of the brain surgery operations are carried out by utilizing classical surgery methodologies and equipment. Although related literature includes studies on the robotization of brain surgery systems by the help of technological advancements, these applications mostly focused on the integration of robot manipulators that are designed for industrial automation into the medical area. Thus it can be clearly seen that, there exist lack of robot manipulators that are specifically designed for brain surgery applications, have necessary precision requirements and workspace constraints. In light of this, evaluating its preprototype performance, current study focuses on the improvement of a spherical parallel manipulator structure that was designed for positioning in robotic brain biopsy by taking operation efficiency, system reliability, workspace constraints and ease of manufacturing into consideration.