Design of a new gravity balanced parallel mechanism with Schönflies motion

2016 ◽  
Vol 230 (17) ◽  
pp. 3111-3134 ◽  
Author(s):  
Long Kang ◽  
Se-Min Oh ◽  
Wheekuk Kim ◽  
Byung-Ju Yi
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Force Transmission ◽  
Kinematic Modeling ◽  
Potential Applications ◽  
Structure Description ◽  
Grassmann Line Geometry ◽  
Schönflies Motion ◽  
Forward Kinematic

In this paper, a new gravity-balanced 3T1R parallel mechanism is addressed. Firstly, structure description, inverse and forward kinematic modeling are performed in detail. Secondly, Jacobian derivation based on screw theory and singularity analysis using Grassmann Line Geometry is performed, and then optimal kinematic design with respect to workspace size, kinematic isotropy and maximum force transmission ratio are conducted. Thirdly, the gravity balancing design using both counterweights and springs is proposed and a prototype of this mechanism is also presented. Results of analysis show that the proposed mechanism has quite a few potential applications.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2015 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between pure translation (3T) and pure rotation (3R) motion. This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraint of the parallel mechanism covering both 3T and 3R motion. Following these screw theory based motion/force transmission equations are obtained and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the metamorphic parallel mechanism. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism (MPM) which can switch its motion between pure translation (3T) and pure rotation (3R). This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable, and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraints of the parallel mechanism covering both 3T and 3R motion. Following this, screw theory based motion/force transmission equations are obtained, and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the MPM. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Development of a novel two-limbed parallel mechanism having Schönflies motion

2014 ◽  
Vol 229 (1) ◽  
pp. 136-154 ◽  
Author(s):  
Sung Mok Kim ◽  
Kyoosik Shin ◽  
Byung-Ju Yi ◽  
Wheekuk Kim
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Model ◽  
Singularity Analysis ◽  
Short Description ◽  
High Potential ◽  
Haptic Device ◽  
Line Geometry ◽  
Grassmann Line Geometry ◽  
Schönflies Motion ◽  
Very High

This paper introduces a novel parallel mechanism having Schönflies motion. The mechanism consists of only two RRPaR-type limbs. After a short description of its structure, its position analysis is conducted and its screw-based kinematic model is derived. Next, its singularity analysis is performed via Grassmann line geometry and then its optimal kinematic characteristics are examined with respect to workspace size and isotropy property. The results show that the proposed parallel mechanism has a very high potential to be used as a manipulator or a haptic device. A prototype of this mechanism was developed and tested to corroborate its performance.

Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mohammad H. Abedinnasab ◽  
Daniel Lichtblau
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
Input Output ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Novel Method ◽  
Schönflies Motion

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kristan Marlow ◽  
Mats Isaksson ◽  
Jian S. Dai ◽  
Saeid Nahavandi
Keyword(s):  
Performance Measures ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Force Transmission ◽  
Six Degrees Of Freedom ◽  
Lower Mobility ◽  
Transmission Ability

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

scholarly journals Kinematic analysis of a novel 3-CRU translational parallel mechanism

2015 ◽  
Vol 6 (1) ◽  
pp. 57-64 ◽  
Author(s):  
B. Li ◽  
Y. M. Li ◽  
X. H. Zhao ◽  
W. M. Ge
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Reachable Workspace ◽  
Potential Applications ◽  
Moving Platform ◽  
And Performance

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Alon Wolf ◽  
Daniel Glozman
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Community Research ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Equilibrium Equations ◽  
Six Degrees Of Freedom ◽  
Singular Configurations

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

On the Design of Singularity-Free Cable-Driven Parallel Mechanism Based on Grassmann Geometry

2012 ◽  
Author(s):  
Yu Zou ◽  
Yuru Zhang ◽  
Yaojun Zhang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Geometric Meaning ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Singular Configurations ◽  
Negative Effect ◽  
Grassmann Line Geometry ◽  
Grassmann Geometry

This paper deals with the design of singularity-free cable-driven parallel mechanism. Due to the negative effect on the performance, singularities should be avoided in the design. The singular configurations of mechanisms can be numerically determined by calculating the rank of its Jacobian matrix. However, this method is inefficient and non-intuitive. In this paper, we investigate the singularities of planar and spatial cable-driven parallel mechanisms using Grassmann line geometry. Considering cables as line vectors in projective space, the singularity conditions are identified with clear geometric meaning which results in useful method for singularity analysis of the cable-driven parallel mechanisms. The method is applied to 3-DOF planar and 6-DOF spatial cable-driven mechanisms to determine their singular configurations. The results show that the singularities of both mechanisms can be eliminated by changing the dimensions of the mechanisms or adding extra cables.

scholarly journals Kinematic analysis of a novel 2-PrRS-PR(P)S metamorphic parallel mechanism

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988977
Author(s):  
Kun Ma ◽  
Hongwei Ma ◽  
Haibo Tian
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Three Dimensional ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Functional Requirements ◽  
Inverse Kinematic Problem ◽  
Loop Equation ◽  
Metamorphic Mechanism ◽  
Forward Kinematic

Lower mobility parallel mechanisms have been developed in different structures and widely applied in industry, but still have disadvantages in various tasks and functional requirements. A 2-PrRS-PR(P)S metamorphic parallel mechanism with two working configurations and a transiting configuration is presented. First, the architecture and the way of metamorphosis about the mechanism are described in detail. The mobility of the metamorphic parallel mechanism is obtained with screw theory. Furthermore, the parasitic motions in different configurations are derived based on the geometry constraint conditions. Both the inverse kinematic problem and forward kinematic problem of the mechanism are investigated by the closed-loop equation and validated via numerical examples. Then, the velocity and acceleration in two working configurations are obtained by the derivation of the inverse kinematic problem. Finally, the reachable orientation workspaces are discussed using the three-dimensional search method in different configurations. A comparison with the 3-PRS PM without metamorphic mechanism in workspace is presented and an example of the metamorphic parallel mechanism in robotic supporting leg is presented. The above analyses provide theoretical foundations for application of this mechanism.

Instantaneous Kinematics and Singularity Analysis of a Novel Three-Legged Mobile Robot With Active S-R-R-R Legs

2008 ◽  
Author(s):  
Ping Ren ◽  
Dennis Hong
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Body ◽  
Jacobian Matrices ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Grassmann Line Geometry ◽  
Actuation Scheme ◽  
Complete Investigation

STriDER (Self-excited Tripedal Dynamic Experimental Robot) is a unique three-legged walking robot that utilizes its innovative tripedal gait to walk. Previous work on the kinematic analysis of STriDER mainly focused on solving the forward and inverse displacement problems. As a continuation, this paper addresses the instantaneous kinematics and singularity analysis. The kinematic configuration of STriDER is modeled as a three-legged in-parallel manipulator when all three feet of the robot are in contact with the ground without slipping. The results obtained from this study can be implemented to the velocity control and the resistance of disturbance forces, thus improving the motion accuracy and stability of the robot. By using screw theory, the screw-based Jacobian matrices of the manipulator can be derived since the forward displacement problems have already been solved. Based on these Jacobian matrices, the transformation equations from the active joint rates to the velocities of the body and vice versa are derived. Then, a complete investigation on the identification and elimination of singularities is presented. Unlike serial manipulators, in-parallel manipulators have two types of singularities, i.e., forward and inverse singularities. The inverse singularities are identified by checking the singular configurations of individual legs and the determinant of the inverse Jacobian matrix. By using Grassmann line geometry, the analytical conditions under which the forward singularities occur are obtained. A study on each case of these singular configurations shows that the redundant-actuation scheme of the active joints can effectively eliminate forward singularities.

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