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.

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

2005 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Xi J. Guo
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Mechanisms ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Family ◽  
Rear Part ◽  
Kinematic Analyses ◽  
Lower Mobility

In the family of lower-mobility (degrees of freedom Nf&lt;6) parallel mechanisms, there is a class of mechanisms whose degrees of freedom equal the number of single-degree-of-freedom pairs in each limb. This paper proposes a novel forward/reverse kinematic analyses method for this class of mechanisms, which can build Nf×Nf square Jacobian matrix and Nf×Nf×Nf cubic Hessian matrix. Thus both forward/reverse velocity and acceleration analyses for this class of mechanisms are derivable. In this method, the formulas 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 pairs), the more effective the method is. In the rear part of the paper, a 5-DOF mechanism 3-RCRR is analyzed as an example.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Rank Deficiency ◽  
Actuation Redundancy ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Lower Mobility

This paper investigates the behavior of a type of parallel mechanisms with a central strut. The mechanism is of lower mobility, redundantly actuated, and used for sprained ankle rehabilitation. Singularity and dexterity are investigated for this type of parallel mechanisms based on the Jacobian matrix in terms of rank deficiency and condition number, throughout the workspace. The nonredundant cases with three and two limbs are compared with the redundantly actuated case with three limbs. The analysis demonstrates the advantage of introducing the actuation redundancy to eliminate singularities and to improve dexterity and justifies the choice of the presented mechanism for ankle rehabilitation.

A New Index of Static Actuation Force Sensitivity of Mechanisms Based on Unified Forward Jacobian Matrix

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Xu Wang ◽  
Weizhong Guo ◽  
Youcheng Han
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Constraints ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Actuation Force ◽  
Force Sensitivity ◽  
Differential Operation ◽  
Static Equation ◽  
Pose Optimization

Abstract This paper proposes a novel performance index, which is called static actuation force sensitivity (SAFS), to investigate the response of the actuation forces when the amplitude of the suffered load of the end-effector has a change. Smaller SAFS can protect the actuations, and the load is mainly suffered by the structural constraints. This work starts with the construction of the unified forward Jacobian matrix of both serial and parallel mechanisms by screw theory. Then, with the forward Jacobian matrix, the inverse static equation is established. SAFS is thus introduced by the “partial differential” operation on the inverse static equation. SAFS is only related to the position of the whole mechanism and the direction of the suffered load, but not related to the detailed value of the amplitude of the load and the detailed value of the actuation forces; thus, SAFS can reveal the essence of static force capacities of the mechanisms. The example mechanism (namely, the 3revolute-prismatic-spherical (RPS) parallel mechanism) is used to illustrate the distribution of SAFS both over the workspace and at a certain pose. The analysis method of SAFS and the proposed index are expected to be applied to the pose optimization in the motion planning of the mechanisms to protect the actuations.

A Family of Novel Lower-Mobility Decoupled Parallel Mechanisms

2007 ◽  
Author(s):  
Daxing Zeng ◽  
Sijun Zhu ◽  
Zhen Huang
Keyword(s):  
Real Time ◽  
Basic Feature ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Real Time Control ◽  
Motion Feature ◽  
Time Control ◽  
Fixed Base ◽  
Lower Mobility ◽  
Moving Platform

This paper presents a family of novel lower-mobility decoupled parallel mechanisms (DPMs), which consists of one 5-DOF (degree of freedom) DPM, two 4-DOF DPMs, three 3-DOF DPMs, and three 2-DOF DPMs. The basic feature of this family is that the moving platform and the fixed base of the DPMs are connected by two limbs and the motion of the moving platform is fully decoupled. Then the constraint screw method is used to analyze the motion feature of all DPMs presented in this paper. The mobility of these DPMs has also been calculated by the Modified Grubler-Kutzbach criterion. All the DPMs in this paper are simple and no computation is required for real-time control.

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.

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulators

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
New Approach ◽  
Kinematic Chains ◽  
Lower Mobility ◽  
Acceleration Analysis ◽  
Definition Of ◽  
Closure Constraints

This paper presents a new approach to the velocity and acceleration analyses of lower mobility parallel manipulators. Building on the definition of the “acceleration motor,” the forward and inverse velocity and acceleration equations are formulated such that the relevant analyses can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

scholarly journals Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

2020 ◽  
Author(s):  
Peng Sun ◽  
Yanbiao Li ◽  
Ke Chen ◽  
Wen-Tao Zhu ◽  
Qi Zhong ◽  
...  
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Screw Theory ◽  
Hessian Matrix ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Kinematics Analysis ◽  
Hybrid Mechanisms ◽  
Parallel Configuration

Abstract The advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. First, according to the kinematics analysis of serial mechanisms, the basic principles of Lie groups Lie algebras in dealing with the spatial switching and differential operations of screw vectors are briefly explained. Then, based on the standard ideas of Lie operations, the method for kinematics analysis of parallel mechanisms is derived, and Jacobian matrix and Hessian matrix are formulated both recursively and in closed form. After that, according to the mapping relationship between the parallel joints and the corresponding equivalent series joints, a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are studied. A case study is performed to verify the calculated matrices, in which a humanoid hybrid robotic arm with the parallel-series-parallel configuration is taken as an example. Simulation experiment results show that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practicable.

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.

scholarly journals Singularity analysis of the H4 robot using Grassmann–Cayley algebra

Robotica ◽  
2012 ◽  
Vol 30 (7) ◽  
pp. 1109-1118 ◽  
Author(s):  
Semaan Amine ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Daniel Kanaan
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Analysis Method ◽  
Rank Deficiency ◽  
Constraint Analysis ◽  
Cayley Algebra ◽  
Lower Mobility ◽  
Grassmann Cayley Algebra

SUMMARYThis paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann–Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

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.

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