Three-legged Parallel Manipulator Research Articles

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.

Kinematics of a Class of Three-Legged Parallel Manipulators by Means of Screw Theory

This work is devoted to the velocity and acceleration analyses of a class of three-legged parallel manipulators. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. With the purpose to exemplify the application of the method, a case study is included. The example consists of solving the kinematics of a 3-CRS (Cylindrical + Revolute + Spherical) parallel manipulator. Furthermore, the numerical results obtained via screw theory are verified with the aid of commercially available software.

Classification of Screw Systems Composed of Three Planar Pencils of Lines for Singularity Analysis of Parallel Mechanisms1

Screw systems composed of (the sum of) three planar pencils of lines are closely related to the singularity analysis of a number of three-legged parallel manipulators (PMs) in which the passive joints in each leg are a spherical joint and a single-DOF (degree of freedom) kinematic joint or generalized kinematic joint. This paper systematically classifies the screw systems composed of three planar pencils of lines based on the intersection of two planar pencils of lines, the classification of screw systems of order 2, and the reciprocal screw system of the three planar pencils of lines. The classification in this paper is more comprehensive than those in the literature. The above results are illustrated using CAD figures. This work may help readers better understand the geometric characteristics of singular configurations of a number of three-legged parallel manipulators.

Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator

In this work the jerk analysis of a 3-RRPS parallel manipulator to realize six degrees of freedom is approached by means of the theory of screws. The input/output equations of velocity, acceleration and jerk of the moving platform with respect to the fixed platform are obtained systematically by resorting to reciprocal-screw theory. A numerical example is included in order to show the application of the method of kinematic analysis. Furthermore, the numerical results obtained via screw theory are satisfactorily compared with simulations generated with the aid of commercially available software.

Kinematics of an asymmetrical three-legged parallel manipulator by means of the screw theory

Abstract In this work the kinematics of a three-legged parallel manipulator with asymmetrical limbs and decoupled motions over its moving platform is investigated by means of the theory of screws. The solution of the forward displacement analysis (FDA) is presented in echelon-form solution using a novel procedure based on simple geometric constraints, thus all the feasible locations of the moving platform, with respect to the fixed platform, are computed given a set of generalized coordinates. After, the velocity and acceleration analyses are carried out using the theory of screws. Finally, a numerical example is included and the results obtained via the screw theory are verified with the aid of special commercially available software like MSC.Adams©.

Direct position analysis of parallel manipulators which generate SP-2PS structures

The determination of the assembly modes of the parallel structures with three legs of type PS or SP (P and S stand for prismatic pair and spherical pair, respectively) consists of solving the direct position analysis of all the three-legged parallel manipulators which have, in each leg, one not actuated prismatic pair, one not actuated spherical pair and one or two one-dof actuated pairs of any type, placed along the leg in any order. There are two types of such structures: (i) 3PS structures and (ii) SP-2PS structures. The procedure to determine the assembly modes of the SP-2PS structures has not been presented yet, in the literature. This paper presents the analytic form determination of the assembly modes of the SP-2PS structures. In particular, the closure equations of a generic SP-2PS structure will be written and their solution will be reduced to the solution of an eight-degree univariate polynomial equation with real coefficients. Finally, the proposed algorithm will be applied to a real case. The result of this study is that the assembly modes of any SP-2PS structure are at most eight, and the end-effector poses, which solve the direct position analysis of the parallel manipulators that generate those structures, are also eight.

Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators

A wide family of parallel manipulators (PMs) is the one that groups all PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen.

Instantaneous kinematics and singularity analysis of three-legged parallel manipulators

Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. Singularity analysis is performed under three categories, namely forward, inverse and combined singularities. A new concept of Passive Joint Plane is introduced to correlate the physical structure of the manipulator and these geometric conditions. In the inverse kinematic analysis, a new approach is introduced. At each leg end point a characteristic parallel- epiped is defined whose sides are the linear velocity components from three main joints of the leg. An inverse singularity occurs when the volume of this parallelepiped becomes zero. Examples are demonstrated using RRRS and RPRS-type parallel manipulators.

Design and kinematics of a three-legged parallel manipulator

This paper investigates the kinematics and stiffness of an isotropic three-legged manipulator having six degrees of freedom. Rotary motors at the base rotate the tool by using the extensible legs as drive shafts. The manipulator has the positional stiffness of a parallel manipulator and the rotational stiffness of a serial manipulator. Low inertia results from having only three legs and having three motors fixed at the base. The inverse kinematics are obtained in closed form. Singularities are characterized for the case of concentric u-joints at the tool. These singularities yield the constraint singularities of a related 3-universal-prismatic-universal translational manipulator.

Fabrication of Non-Assembly Mechanisms and Robotic Systems Using Rapid Prototyping

In this paper, the application of Rapid Prototyping in fabricating non-assembly robotic systems and mechanisms is presented. Using two Rapid Prototyping techniques, Stereolithography and Selective Laser Sintering, prototypes of mechanical mobile joints were fabricated. The designs of these component joints were then used to fabricate the articulated structure of experimental prototypes for two robotic systems: (1) a three-legged parallel manipulator, (2) a four degree-of-freedom finger of a five-fingered robotic hand. These complex multi-articulated, multi-link, multi-loop systems have been fabricated in one step, without requiring assembly while maintaining their desired mobility. The feasibility and usefulness of Rapid Prototyping as a method for the fabrication of these non-assembly type mechanisms and robotic systems is the focus of this work.