A Novel Spherical Parallel Manipulator with Circular Guide

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°.

Spherical parallel manipulators (SPMs) are used to orient a tool in the space with three degrees of freedom exploiting the strengths of a multi-limb architecture. On the other hand, the performance of parallel kinematics machines (PKMs) is often affected by the occurrence of different kinds of singular configurations. The paper aims at characterizing a class of SPMs for which all singularities come to coincide and a single expression is able to describe all the singular configurations of the machines. The study is focused on a class of SPMs with 3-RFR topology (Revolute-Planar-Revolute pairs for each of the three limbs) addressing the mobility and singularity analysis by means of polynomial decomposition and screw theory. The neatness of the equations that are worked out, expressed in a robust formulation based on rotation invariants, allows a straightforward planning of singularity free tasks and simplifies the synthesis of dexterous machines.

This paper deals with the forward displacement analysis and singularity analysis of a 2-DOF 5R spherical parallel manipulator. An alternative formulation of the kinematic equations of the 2-DOF spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the FDA of the 2-DOF spherical parallel manipulator. It is proved that the formula is associated with the same assembly mode and working mode as the reference configuration of the spherical parallel manipulator. Unlike other parallel manipulators, the 2-DOF 5R spherical parallel manipulator always undergoes self-motion in a Type 2 singular configuration, and the 3R leg of the 2-DOF spherical parallel manipulator also always undergoes self-motion in a Type 1 singular configuration.

A novel spherical parallel manipulator (SPM), named Riflex, is designed and studied in this paper. Compared with the traditional SPMs, this novel SPM is composed of one rigid supporting limb and three flexible limbs, this type SPM has a great potential application in medical equipment and rehabilitation robots. The kinematics analysis, the numerical simulation of the kinematic analysis and the potential applications of the parallel manipulator are presented in this paper.

This work deals with the forward and inverse kinematic analysis of a coaxial spherical parallel manipulator (SPM) by using the Euler angles representation for the mobile’s platform orientation. A unique solution for the inverse and forward kinematic problem which corresponds with the assembly mode of a physical prototype is considered. The screw theory is then used to derive the Jacobian matrix as well as to carry out the velocity analysis. Finally, the solutions from both analysis are compared with numerical results obtained by simulation using ADAMS View software for different position and velocity trajectories, showing the validity of the obtained results.

Spherical parallel manipulators (SPMs) have a wide range of applications such as orienting devices and robotic wrists. In this paper, the 3 independent rotational characteristics of SPMs are divided into two groups orienting from the upper and lower parts of the SPMs respectively. The type synthesis of such SPMs is performed by using upper-lower combination rules and the axis movement theorem. The concept of parallel mechanism with symmetrical characteristics is introduced. Then, some novel SPMs with symmetrical characteristics are represented by introducing the PR joint and the composite joints deduced from the simple joints. Finally, the different geometrical conditions of assembly for parallel manipulators (PMs) with different characteristics are discussed. The concept of the upper-lower combination may provide a new idea for type synthesis of parallel mechanisms.

This paper presents the stiffness analysis and design of a 3-DOF parallel robot with one constraining leg, which takes into account of elastic deformations of joints and links. The parallel manipulator in this study is made up of three SPS (Spherical-Prismatic -Spherical) legs and one UP (Universal-Prismatic) leg at the center. The role of the UP leg constrains the motion of the moving platform to 3-DOF and the three SPS legs drives the moving platform by three linear actuators. The stiffness matrix is derived as follows. The reaction forces due to actuations and constraints in each serial chain are determined by making use of the theory of reciprocal screws. The stiffness of this manipulator is modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations and constraints. A general 6times6 stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. Then the compliance of each spring is precisely determined by modeling the compliance of joints and links in a serial chain. Using the suggested methodology, the stiffness of the 3-DOF parallel robot with one constraining leg has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.

² This paper deals with a spherical parallel manipulator developed for a master device, used in a teleoperation system for surgical application. The aim is to improve the calculation of the direct kinematic model (DKM) even when the parallel manipulator is i n a singular configuration by using an extra sensor for a passive joint. A new simple approach for the DKM calculation of the haptic device, in order to meet requirement of real time applications, is developed. The measure of a passive joint's angle reduc es the calculation time and improves the accuracy of the direct model particularly in the vicinity of the singular positions. Experiments were conducted on tele -operation system despite of the presence of singularities in the master workspace. The obtaine d results demonstrate the feasibility of the approach. I. I NTRODUCTION The use of parallel structure as haptic device in tele -operation systems has substantially increased in past years, because parallel mechanisms have the advantage of being accurate and rig id. Tobergte et al. [1] proposed a delta parallel structure as haptic device called sigma.7 to control the DLR lightweight robot MIRO [2]. Ma et al. [3] have experiment a 4 -DOF haptic device in a virtual environment. The spherical parallel manipulator ( SPM ) is class of the parallel robot that has a fixed center of rotation. It was used by Gosselin et al . to control the orientation of a camera [4]. A new SPM is presented in this paper used as a haptic interface in a tele -operation system for a surgical application. The parallel robots suffer from the parallel singularity. This type of singularity, for the case of SPM, appears inside the workspace and generates large actuator torques and a loss of stiffness. The forces (and/or) torques applied to the end -effector, when it is located in parallel singularity, cannot be balanced by the tor ques produced by the actuators . Therefore, uncontrollable movements appear instantly . In the literature, several studies have attempted to remove this type of singularity of the workspace by proposing an optimized structure [5]-[6]. However by improving the kinematic behavior, the parallel robot structure often becomes larger and a problem of interference

This paper focuses on the systematic type synthesis of parallel robot manipulators by using new structural formulas based on the screw theory. New structural formulas as a total number of screw in kinematic pairs , number of screws with variable pitch , total number of screws that represent the contact geometry of lower and higher joint elements (t), mobility equation for robot manipulators (M), dimension of the closed loop , motion of end effector of parallel manipulator , number degree of freedom of kinematic pairs , refers to find the kinematic structure of robot manipulators realizing a specified motion requirement. Twenty kinematic pairs with structural parameters are introduced. History of six structural formulas using for structural synthesis of parallel robot manipulators from space and different subspaces are presented as a table with equations, authors, years and some commentaries. The structural synthesis approach is based on the elementary notions of screw theory. Using the proposed of structural formulas approach, families of platform manipulators are constructed from a set of structural units. This paper is appropriate for engineers with interest in robotics, rovers, space docking parallel manipulators and screw theory.

A systematic analytical method, based on the theory of screws, is presented for identification of limb structures of general and over-constrained 3-degree-of-freedom (DOF) translational parallel manipulators. Given a system of wrenches of constraint, the corresponding reciprocal basis screws are determined. Then, the joint screws of a limb are obtained by a linear combination of these basis screws. Feasible limbs that can be used for construction of translational platforms are enumerated according to the type of constraint and the number of joints making up the limbs. © 2004 Wiley Periodicals, Inc.

The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

In this paper the kinematic analysis of a six-legged robot, hereafter named Hex-piderix, is carried out. A three revolute (3R) chain has been chosen for each limb in order to mimic the leg structure of an insect. The rotation matrix, with unitary vectors, and the Denavit-Hartenberg (D-H) conventions are used to find the pose of the thorax. The problem of inverse position is solved by geometrical analysis. The direct and inverse infinitesimal kinematics are obtained by the reciprocal screw theory, considering a suction cup attached to each leg and modelling it as a UP linkage. A numerical example of the thorax pose was made by solving the equations obtained from the direct position analysis. The equations of the inverse position analysis were solved to obtain the angles of the joints. Finally, the velocity values of the thorax obtained from the infinitesimal kinematics were validated by simulating the movements of Hex-piderix using specialized software.

The parallel manipulators with n<6 spherical joint-prismatic joint-spherical joint (SPS) type active legs and one passive constrained leg have attracted more attention and been used in many practical applications. This kind of parallel manipulator has a larger capability of load bearing and a simple structure of active leg. The paper used 4-SPS/PS four degree-of-freedom (DOF) parallel manipulator for the simulation of ship's heave and swing motion. Mobility property of the 4-SPS/PS parallel manipulator is analyzed by screw theory. The inverse position kinematics model is established and the analytical solution is obtained. It uses extra sensor and Sylvester resultant elimination to derive analytical solutions of forward position kinematics including two real solutions and two imaginary solutions, and uses vector cross product to derive the Jacobian matrix of 4-SPS/PS parallel manipulator. Furthermore, it introduces three performance indicators to analyze the singularity. In order to obtain accurate analysis results of singularity, it calculates the minimum singular value, condition number and manipulability degree of Jacobian matrix for different combination of pose, respectively.

The instantaneous kinematics of a special 3-UPU parallel platform manipulator is discussed in this paper. First, the instantaneous motions of the 3-UPU manipulator in four position and a special manipulator are studied by reciprocal screw theory. Then, the principal screws in one of four position are obtained. It is shown that the moving platform has five DOF (degrees of freedom) in the initial position or after a translation along the Z-axis; in the generic position, the mechanism only has three DOF, moreover the three DOF characteristics are difference in different position. The instantaneous kinematic characteristics of alike 3-UPU mechanisms are very different in different position and special structure. The results presented in this paper are important to the use of alike 3-UPU parallel manipulator and contribute to the mechanism theory.

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator