Forward kinematics analysis of parallel mechanisms with restricted workspace

2014 ◽  
Vol 229 (14) ◽  
pp. 2561-2572 ◽  
Author(s):  
Mingchao Geng ◽  
Tieshi Zhao ◽  
Chang Wang ◽  
Yuhang Chen ◽  
Erwei Li
Keyword(s):  
Jacobian Matrix ◽  
Search Method ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Iterative Search ◽  
Newton Raphson ◽  
Equivalent Method ◽  
Quasi Newton

The iterative search method (Newton-Raphson or Quasi-Newton) is an important numerical method for solving the forward kinematics problem of parallel mechanisms. But there may be a failure when the iterative search method solves the forward kinematics problems of a class of mechanisms, whose workspace is restricted. The extreme displacement singularity in the limbs is one reason for the workspace restriction. An equivalent method is proposed to remove the extremely displacement singularity in the limbs, and the forward kinematics solutions of two representative 6 degree of freedom mechanisms are given to illustrate the mechanism equivalence. For the coupled fewer degree of freedom mechanisms, the coupled motion is another reason for the workspace restriction. The virtual mechanism method and modified Jacobian matrix method are applied to solve the forward kinematics problems of this class of mechanisms. Numerical examples are given to validate the theories proposed above.

A novel 4-RRCR parallel mechanism based on screw theory and its kinematics analysis

2012 ◽  
Vol 227 (9) ◽  
pp. 2039-2048 ◽  
Author(s):  
Sheng Guo ◽  
Congzhe Wang ◽  
Haibo Qu ◽  
Yuefa Fang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Elimination Method ◽  
Direct Kinematics

In this article, a novel 4-RRCR parallel mechanism is introduced based on screw theory, and its kinematics and singularity are studied systematically. First, the degree of freedom analysis is performed using the screw theory. The formulas for solving the inverse and direct kinematics are derived. Second, a recursive elimination method is proposed to solve the Jacobian matrix based on the algebra operation of reciprocal product. Then, three kinds of singularity, i.e. limb, platform, and actuation singularities are analyzed. Finally, the analysis proves that the proposed mechanism possesses two advantages of simple forward kinematics and no platform singularity.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

scholarly journals Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985307
Author(s):  
Xing Zhang ◽  
Dejun Mu ◽  
Yuze Liu ◽  
Jie Bi ◽  
Hongrui Wang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Type Synthesis ◽  
Lie Group Theory ◽  
Revolute Joints ◽  
Pick And Place ◽  
Pick And Place Operation

This article proposes a family of spatial three translational and one rotational parallel mechanisms (PMs) for pick-and-place operation. Their features are one independent rotation of the mechanism with four identical limbs, which are provided by the four revolute joints on the moving platform. The rotational capability of the PMs has a range of at least 180°. This article focuses on the synthesis of the PMs and kinematics analysis of the 4- P(2-SS)R parallel mechanism. First, based on the Lie group theory, three parallelograms are used in designing the PMs. The limbs are listed and two types of three translational and one rotational PMs are synthesized. Then, a typical 4- P(2-SS)R PM is selected, the 6 × 6 Jacobian matrix and the 6 × 6 × 6 Hessian matrix of the mechanism are derived for solving the displacement, velocity, and acceleration of the mechanism. Finally, singularity configurations are disclosed from the 6 × 6 Jacobian matrix, and the workspace of the mechanism is provided to illustrate the high rotational capability.

Forward Kinematics Analysis and Experiment of Small-Caliber Well Rescue System

2014 ◽  
Vol 945-949 ◽  
pp. 1426-1429
Author(s):  
Xiu Juan Sun ◽  
Chuan Jiang Wang ◽  
Jian Wu
Keyword(s):  
Degree Of Freedom ◽  
Experimental Results ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Experimental Prototype ◽  
Deep Well ◽  
Mechanical Component ◽  
Rescue Experiment ◽  
Rescue System ◽  
Rescue Mechanism

As for the new designed small-caliber well rescue system for the fallen person in deep well, we made a detailed description about the rescue mechanism, which was composed of framework, anchorage set, stretching arm and clasp arm, and illustrated the function of each mechanical component. Moreover, we deduced the forward kinematics matrices of the clasp arm and the stretching arm, and analyzed and provided the parameters of each degree of freedom. Meanwhile, the experimental prototype of the rescue system was designed and the imitated rescue experiment for a doll was fulfilled. The experimental results show that the rescue system is feasible in small caliber deep well rescue.

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

2010 ◽  
Vol 17 (6) ◽  
pp. 1264-1270 ◽  
Author(s):  
Chi-fu Yang ◽  
Shu-tao Zheng ◽  
Jun Jin ◽  
Si-bin Zhu ◽  
Jun-wei Han
Keyword(s):  
Parallel Manipulator ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Newton Raphson ◽  
Raphson Method

On the Force Capabilities of Two-Degree-of-Freedom Planar Parallel Mechanisms Equipped With Torque Limiters

2013 ◽  
Author(s):  
Wei Chen ◽  
Clément Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Joint Torque ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Human Beings ◽  
Safety Index ◽  
End Effector ◽  
Two Degree Of Freedom ◽  
Insight Into

Safety is the most important issue that should be considered when designing collaborative robots that are intended to physically interact with humans. This paper investigates the force capabilities of two-degree-of-freedom planar parallel mechanisms that are equipped with torque limiters (safety clutches). Joint torque limiting devices are used in these mechanisms in order to limit the forces that the robot can apply to its environment. Such devices aim at ensuring the safety of the human beings interacting with the robot. However, because the torque-limiting devices are mounted at the joints of the robot, the end-effector force capabilities induced by these devices are dependent on the pose (Jacobian matrix) of the robot. Therefore, the characteristics of the torque limiting devices must be determined at the design stage in order to ensure safety and maximize effectiveness in all possible poses of the robot. Two types of planar two-degree-of-freedom parallel mechanisms are considered in this paper. Their architecture is first described. Then, the force capabilities are studied based on the Jacobian matrices. The maximum force that can be applied at the end-effector for given torque limits (safety index) is determined together with the maximum isotropic force (effectiveness) that can be produced. The ratio between these two forces, referred to as the force efficiency, can be considered as a performance index. Finally, some numerical results are proposed which can provide insight into the design of cooperation robots based on parallel architectures.

A 2-DOF Translational Parallel Manipulator with Passive Universal Joints

2013 ◽  
Vol 278-280 ◽  
pp. 541-545
Author(s):  
Zeng Ming Li ◽  
Bin Bin Peng ◽  
Bao Gang Yang ◽  
Hao Yuan Chen
Keyword(s):  
Spatial Structure ◽  
Bearing Capacity ◽  
Parallel Manipulator ◽  
Simple Structure ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
High Stiffness ◽  
The Stability ◽  
Universal Joints

In the paper, a novel 2-DOF (degree of freedom) plane translational parallel manipulator with passive universal joints and three legs is presented. Firstly, the 2-DOF translational parallel manipulator which has the spatial structure and high bearing capacity in the direction perpendicular to the kinematics plane is described. Then, the kinematics analysis of the 2-DOF parallel manipulator, which include inverse and forward solutions, are studied in detail, and the Jacobian matrix of the parallel manipulator is also derived based on it. Lastly, to improve the stability and bearing capacity further, the symmetric mechanisms with four legs and passive universal joints are constructed by adding a leg in parallel. The proposed 2-DOF parallel manipulator not only has the simple structure, but high stiffness especially in the direction perpendicular to kinematics plane for its spatial arrangment and passive universal joints.

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