A Novel Three-DOF Translational Platform Mechanism and its Kinematics

2000 ◽  
Author(s):  
Tie Shi Zhao ◽  
Zhen Huang
Keyword(s):  
Parallel Manipulator ◽  
Polynomial Equation ◽  
Forward Kinematics ◽  
Three Dimension ◽  
Parallel Mechanisms ◽  
Degree Polynomial ◽  
Numerical Examples ◽  
Mechanism Model

Abstract To enrich the type of three-DOF parallel mechanisms, a novel 3-RRC platform mechanism model is presented in this paper. The upper platform of this 3-DOF parallel manipulator can realize three-dimension translations without any rotations. The solutions are developed for both the inverse and forward kinematics. The inverse position kinematics produces two solutions for each limb of manipulator. The forward position kinematics is reduced to an eighth-degree polynomial equation. The velocity and acceleration analyses are also given. Some numerical examples and relational curves are presented finally.

Singularity-locus expression of a class of parallel mechanisms

Robotica ◽  
2002 ◽  
Vol 20 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Polynomial Equation ◽  
Geometric Parameters ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Degree Polynomial ◽  
Singular Configurations ◽  
Singularity Locus ◽  
Orientation Parameters

In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform position parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.

Forward Kinematics in Polynomial Form of the General Stewart Platform1

1998 ◽  
Vol 123 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Parallel Manipulator ◽  
Polynomial Equation ◽  
Polynomial Form ◽  
Floating Point ◽  
Forward Kinematics ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
General Geometry ◽  
Floating Point Computation

The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

Closed-Form Direct Position Analysis of a 5–5 Parallel Mechanism

1993 ◽  
Vol 115 (3) ◽  
pp. 515-521 ◽  
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Closed Form ◽  
Parallel Mechanism ◽  
General Feature ◽  
Polynomial Equation ◽  
Stewart Platform ◽  
Parallel Mechanisms ◽  
Complex Field ◽  
Output Link ◽  
Degree Polynomial ◽  
Displacement Analysis

The paper presents the closed form direct displacement analysis for a class of Stewart platform-type parallel mechanisms whose general feature consists of six legs which meet five distinct points both in the base and in the movable output link. Out of the two possible arrangements, only one is here analyzed in detail. Given a set of actuator displacements the analysis provides all the possible locations of the platform relative to the base. The analysis results in a 40th degree polynomial equation in one unknown. The roots of the equation provide in the complex field forty closures of the mechanism. This new result has been numerically verified by the inverse displacement analysis.

Forward Kinematics of 3-RPS Parallel Mechanisms Using Conformal Geometric Algebra

2017 ◽  
Author(s):  
Ying Zhang ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Duanling Li
Keyword(s):  
Geometric Algebra ◽  
Solution Process ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Solution Procedure ◽  
Conformal Geometric Algebra ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Mathematics Mechanization ◽  
Rotational Angle

In this paper, we propose a novel solution process for the forward kinematics of general 3-RPS parallel mechanisms based on conformal geometric algebra (CGA). First of all, the position of one of the three spherical joints is expressed in the rotational angle about the axis of one kinematic chain RPS. Secondly, the other two spherical joints can be determined by this angle via CGA operation. Thirdly, an explicit 16th-degree univariate polynomial equation is reduced from two geometric constraint equations. At last, one numerical example is employed to verify the solution procedure. The novelties of this paper lie in that (1) the modeling formulation and the elimination procedure have intrinsic geometric intuition due to the use of CGA and (2) the 16th-degree polynomial equation without extraneous roots is explicitly formulated and suitable for implementing the mathematics mechanization of this problem.

Forward Kinematics in Polynomial Form of the General Stewart Platform

1998 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Parallel Manipulator ◽  
Polynomial Equation ◽  
Polynomial Form ◽  
Floating Point ◽  
Forward Kinematics ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
General Geometry ◽  
Floating Point Computation

Abstract The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1686-1703 ◽  
Author(s):  
Mohammad Reza Chalak Qazani ◽  
Siamak Pedrammehr ◽  
Arash Rahmani ◽  
Behzad Danaei ◽  
Mir Mohammad Ettefagh ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
High Acceleration ◽  
Workspace Analysis ◽  
Rotation Symmetric ◽  
Cloud Of Points

SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

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