This paper deals with the optimization of a new redundant spherical parallel manipulator (New SPM). This manipulator consists of two spherical five-bar mechanisms connected by the end-effector, providing three degrees of freedom, and has an unlimited self-rotation capability. Three optimization procedures based on the genetic algorithm method were carried out to improve the dexterity of the New SPM. The first and the second optimizations were applied to a symmetric New SPM structure, while the third was applied to an asymmetric New SPM structure. In both cases, the optimization was performed using an objective function defined by the quadratic sum of link angles. In addition, certain criteria and constraints were implemented. The obtained results demonstrate significant improvements in the dexterity of the New SPM and its capability of an unlimited self-rotate in an extended workspace. A comparison of the self-rotation performances between the classical 3-RRR SPM (R for revolute joint) and the New SPM is also presented.

A 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.

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

In this paper, a novel 3(RPSP)-S fully spherical parallel manipulator (SPM) is introduced. Also, an innovative method based on the geometry of the manipulator is presented for solving the forward position problem of the manipulator. The presented method provides a framework for the future research to solve the forward position problem of the other fully spherical PMs (for examples 3(UPS)-S and 3(RSS)-S). In the proposed method, two coupled trigonometric equations are obtained by utilizing the geometry of the manipulator and Rodrigues' rotation formula. Using Bezout's elimination technique, the two coupled equations lead to a polynomial of degree eight. We show that the polynomial is minimal and optimal. Furthermore, the other method is proposed for selecting an admissible solution of the forward position problem. This algorithm is required to control modeling and dynamic simulations.

This paper discusses the study of a spherical parallel manipulator (SPM) used as a haptic device for tele-operation applications. The SPM presents poor behavior in singular configurations. Redundancy is used to eliminate the parallel singularity without major changes in the mechanical structure. Comparisons in terms of kinematic and dynamic behavior between the non-redundant and redundant SPM are presented. The results prove the advantage of introducing redundancy in the actuator and sensor to improve the behavior of the SPM. A new control strategy for the redundant SPM is also proposed. The control strategy has been successfully tested and validated on a SimMechanics model.

The objective of this article is to present the dimensional synthesis of serial andparallel spherical wrists, an important step in the design process of medical robots. Thisstep is carried out to obtain optimal dimensions of tool-guidance medical robots. Withthis goal, we have first studied the specifications of two robots with different medicalapplications: one for tele-echography examination and one for minimally invasive surgery.Then, we have established that the medical needs expressed by the doctors were verydifferent but the specifications in robotic terms have a lot of common points (kinematics,workspace, bulkiness). For both applications studied, robots need a mobility of threerotations around a fixed point (probe contact point on the patient’s skin or trocarincision). So, a spherical wrist architecture is adapted to their needs. An importantconstraint related to medical applications is that the robot must be compact in order tonot obstruct or collide with its environment (medical personnel or patient). We performdimensional synthesis allowing determination of dimensions of the mechanism for serial andparallel spherical wrists, for a tele-echography robot, and a serial wrist for a minimallyinvasive surgery robot. We use multi-criteria optimization methods minimizing a costfunction to obtain both good kinematic performance and compactness for the architecture.The difficulty/challenge of this design process, depending of the studied applications, isthe choice of efficient criteria describing the performances and the constraints of therobot. The design variables must faithfully represent the specifications of the robot sothat its performance can respond to the medical requirements. We show, here, the differentmethods used for optimizing the chosen kinematic architecture for the particular medicalapplication. These studies lead to prototypes which are validated after medicalexperiments. This process of dimensional synthesis will be applied to other medicalapplications with different sets of specified constraints.

A non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.

In this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663–676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global conditioning index (GCI) of the manipulator is calculated and compared with another SPM. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. A continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano's theorem. The mathematical model is verified by finite element model. Finally, using mathematical model, kinematics stiffness index (KSI), and global stiffness index (GSI) are evaluated.

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipulated. Moreover, a homogeneous workspace can be obtained with Euler parameters for the SPMs, which facilitates the evaluation of dexterity. In this work, the problem of workspace modelling and analysis is formulated in terms of Euler parameters. An equation dealing with boundary surfaces is derived and branches of boundary surface are identified. Evaluation of dexterity is explored to quantitatively describe the capability of a manipulator to attain orientations. The singularity identification is also addressed. Examples are included to demonstrate the application of the proposed method.

In this paper, a novel spherical parallel manipulator and its isotropic design is introduced. This manipulator has good accuracy and relatively a larger workspace which is free of singularities. Utilizing spherical configuration the forward position problem is solved by equivalent angle–axis representation and Bezout's method which leads to a polynomial of degree 8. Two examples are given, one for isotropic and one for nonisotrpoic design. The first case results in eight real solutions, therefore, the polynomial being minimal. Using invariant form, we study acceleration analysis, conditions for singularity and find infinite isotropic structures. Accuracy and workspace analysis are also performed and are shown to have good global conditioning index and relatively large workspace. Using isotropic design and singularity requirements, we show the workspace of isotropic design is free of singularity.

This paper presents a simple methodology for the quantitative and qualitative analysis of the performance of spherical parallel platforms. The quaternion formulation is used to represent the possible rotations, showing the workspace as a three-dimensional (3-D) solid object. The singularities of the platform intersect graphically with its workspace, allowing a graphical study of the mechanism kinematics. The performance criterion considered here has been the local dexterity of the manipulator. This methodology has been used to study and analyze three known orientation parallel platforms: 3-RRR, 3-UPU-wrist, and 2-UPS-1-RU. The objective of this study is to analyze the ability of these platforms to be utilized as mechanisms for the neck and shoulders of humanoid robots. Finally, the forces on actuators in some typical motions for neck and shoulder are plotted.

This paper presents a new method to analyze the closed-form kinematics of a generalized three-degree-of-a-freedom spherical parallel manipulator. Using this analytical method, concise and uniform solutions are achieved. Two special forms of the three-degree-of-freedom spherical parallel manipulator, i.e. right-angle type and a decoupled type, are also studied and their unique and interesting properties are investigated, followed by a numerical example.