Five-Bar Cylinder-Crank Two-DOF Parallel Manipulators for Singularity-Free Path Generation

2009 ◽  
Author(s):  
Hong Zhou ◽  
Swetha Minupuri ◽  
Shilpa Indroju ◽  
Vasuda Gorti
Keyword(s):  
Free Path ◽  
Condition Number ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Path Generation ◽  
Operation Speed ◽  
Proper Design

Parallel manipulators have the merits of high stiffness, load-bearing, operation speed and precision positioning capabilities that are required in many industrial applications. The main challenges for parallel manipulators are their limited workspace and singularity-free path generation capability. This paper is focused on the singularity-free path generation of five-bar cylinder-crank two-DOF parallel manipulators. The linkage feasibility conditions are derived based on the elimination of dead point position within the workspace. The workspace is generated using the curve-enveloping theory. The singularity characteristics and linkage configurations are presented. The singularity-free path generation capability is analyzed. The performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. This paper shows that five-bar cylinder-crank two-DOF parallel manipulators can be used as effective singularity-free path generators if properly designed. The results of this paper provide a useful map for the proper design of this type of parallel manipulator.

Five-Bar Double-Slider Two-DOF Parallel Manipulators for Singularity-Free Path Generation

2008 ◽  
Author(s):  
Hong Zhou ◽  
Kamlesh Borgaonkar ◽  
Govind Raj Venkat Rao
Keyword(s):  
Free Path ◽  
Condition Number ◽  
Parallel Manipulator ◽  
Closed Loop ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Path Generation ◽  
Operation Speed ◽  
Proper Design

Parallel manipulators are closed-loop multi-degree-of-freedom linkages, which have the merits of high stiffness, load-bearing, operation speed and precision positioning capabilities that are required in many industrial applications. The main challenges for parallel manipulators are the limited workspace and singularity-free path generation capability. This paper is focused on the singularity-free path generation of five-bar double-slider two-DOF parallel manipulators. The linkage feasibility conditions are derived based on the elimination of dead point position within the workspace. The workspace is generated using the curve-enveloping theory. The singularity characteristics and linkage configurations are presented. The singularity-free path generation capability is analyzed. The performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. This paper shows that five-bar double-slider two-DOF parallel manipulators can be used as effective singularity-free path generators if properly designed. The results of this paper provide a useful map for the proper design of this type of parallel manipulator.

Cylinder-Slider Parallel Manipulators for Singularity-Free Path Generation

2011 ◽  
Author(s):  
Hong Zhou ◽  
Phani Kumar Mallampati ◽  
Venkata Krishna Perivilli
Keyword(s):  
Free Path ◽  
Condition Number ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Path Generation ◽  
Point Position

A challenge for cylinder-slider parallel manipulators is their limited workspace and singularity-free path generation. In this paper, the linkage feasibility conditions are derived based on the elimination of dead point position within the workspace. The workspace is generated using the curve-enveloping theory. The singularity-free path generation capability is analyzed. The performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. This paper shows that five-bar cylinder-slider parallel manipulators can be used as effective singularity-free path generators if properly designed. The results of this paper provide a useful map for designing this type of parallel manipulator.

Kinematic Inversion of Parallel Manipulators in the Presence of Incompletely Specified Tasks

1990 ◽  
Vol 112 (4) ◽  
pp. 494-500 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Continuous Function ◽  
Condition Number ◽  
Performance Index ◽  
Free Parameter ◽  
Optimization Problem ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Cartesian Coordinates ◽  
Kinematic Inversion ◽  
On Line

In this paper, the kinematic inversion of redundant parallel manipulators in the presence of incompletely specified tasks is formulated as an optimization problem. The performance index used is the condition number of the Jacobian matrix of the manipulator which is a measure of Jacobian invertibility. In order to optimize this index along a partially prescribed Cartesian trajectory, the concept of trajectory map is introduced. It is also shown that the optimum value of the free parameter that minimizes the condition number is not a continuous function of the prescribed Cartesian coordinates. An on-line algorithm producing continuous joint histories is then discussed. This method has been implemented and tested, as illustrated with the results presented here.

Designing a Translational Parallel Manipulator Based on the 3SS Kinematic Joint

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Alfonso Hernández
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Modular Design ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Point Of View ◽  
Pick And Place ◽  
Prismatic Joints ◽  
Singularity Locus ◽  
Kinematic Joint

Abstract Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

Dimensionally Homogeneous Jacobian and Condition Number

2016 ◽  
Vol 836 ◽  
pp. 42-47 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Performance Analysis ◽  
Condition Number ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Moving Platform ◽  
Conditioning Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion

2005 ◽  
Author(s):  
Ofelia Alba-Gomez ◽  
Philippe Wenger ◽  
Alfonso Pamanes
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Jacobian Matrix ◽  
Characteristic Length ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Kinematic Inversion ◽  
Two Indices

This paper investigates the problem of defining a consistent kinetostatic performance index for symmetric planar 3-DOF parallel manipulators. The condition number of the Jacobian matrix is known to be an interesting index. But since the Jacobian matrix is dimensionally inhomogeneous, a normalizing length must be used. This paper proposes two distinct kinetostatic indices. The first one is defined as the reciprocal of the condition number of the Jacobian matrix normalized with a convenient characteristic length. The second index is defined by a geometric interpretation of the “distance” to singularity. The two indices are compared and applied to the kinematic inversion in the presence of redundancy.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

scholarly journals Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Constraint Analysis ◽  
Fixed Direction ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

Unified Solving Jacobian∕Hessian Matrices of Some Parallel Manipulators With n SPS Active Legs and a Passive Constrained Leg

2006 ◽  
Vol 129 (11) ◽  
pp. 1161-1169 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Simple Approach ◽  
Spherical Joint ◽  
Load Bearing ◽  
Prismatic Joint ◽  
First Order ◽  
Partial Differentiation

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

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