scholarly journals A Transmission Quality Index for a Class of Four-Limb Parallel Schönflies Motion Generators

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Guanglei Wu ◽  
Shaoping Bai ◽  
Stéphane Caro
Keyword(s):  
Scalar Product ◽  
Quality Index ◽  
Cross Product ◽  
Parallel Robots ◽  
Uniform Method ◽  
Mobile Platform ◽  
Jacobian Matrices ◽  
Transmission Quality ◽  
Schönflies Motion ◽  
Unit Vectors

This paper presents a uniform method of evaluating both transmission quality and singularity applicable for a class of parallel Schönflies-motion generators (SMGs) with four RRΠRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform (MP). The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Four robots are compared based on the proposed indices as illustrative examples.

Simultaneous base and tool calibration for self-calibrated parallel robots

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 367-374 ◽  
Author(s):  
Guilin Yang ◽  
I-Ming Chen ◽  
Song Huat Yeo ◽  
Wee Kiat Lim
Keyword(s):  
Parallel Robot ◽  
Parallel Robots ◽  
Sufficient Accuracy ◽  
Least Square ◽  
Mobile Platform ◽  
Calibration Model ◽  
End Effector ◽  
The World ◽  
Kinematic Transformation ◽  
Kinematic Errors

In this paper, we focus on the base and tool calibration of a self-calibrated parallel robot. After the self-calibration of a parellel robot by using the built-in sensors in the passive joints, its kinematic transformation from the robot base to the mobile platform frame can be computed with sufficient accuracy. The base and tool calibration, hence, is to identify the kinematic errors in the fixed transformations from the world frame to the robot base frame and from the mobile platform frame to the tool (end-effector) frame in order to improve the absolute positioning accuracy of the robot. Using the mathematical tools from group theory and differential geometry, a simultaneous base and tool calibration model is formulated. Since the kinematic errors in a kinematic transformation can be represented by a twist, i.e. an element of se(3), the resultant calibration model is simple, explicit and geometrically meaningful. A least-square algorithm is employed to iteratively identify the error parameters. The simulation example shows that all the preset kinematic errors can be fully recovered within three to four iterations.

Vectors and Functions and Operators

2020 ◽  
pp. 3-13
Author(s):  
Jochen Autschbach
Keyword(s):  
Linear Algebra ◽  
Scalar Product ◽  
Cross Product ◽  
Eigenvalues And Eigenvectors ◽  
Laplace Operators

This chapter introduces – briefly – vectors and functions and the similarities between them, some basic linear algebra concepts, operators (including the del and Laplace operators), eigenvalues and eigenvectors &eigenfunctions, the scalar (dot) and vector (cross) product between two vectors, the scalar product between two functions, the concepts of normalization, orthogonality, and orthonormality. The concept of an operator is first introduced by considering the rotation and stretching or compression of a vector. It is then generalized to a mathematical prescription that changes a function into another function.

Stiffness estimation of a parallel manipulator using image analysis and camera calibration techniques

Robotica ◽  
2012 ◽  
Vol 31 (4) ◽  
pp. 657-667 ◽  
Author(s):  
Abraham Gonzalez-Hernandez ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Image Analysis ◽  
Camera Calibration ◽  
Parallel Manipulator ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Mobile Platform ◽  
End Effector ◽  
Simple Implementation ◽  
Specific Position ◽  
Calibration Techniques

SUMMARYThis work presents a methodology using image analysis to estimate the experimental stiffness of a parallel robot, Parallix LKF-2040, a 3-degree-of-freedom manipulator. The proposed methodology has a simple implementation and can be applied to different architectures of parallel robots. This methodology uses image analysis and camera calibration techniques to estimate compliant displacements of mobile platform produced by several loads at the end effector level, and calculate stiffness in a specific position of mobile platform. Experimental results are presented for different positions within the workspace.

Kinematics and Stiffness Modeling of a 4-DOF Parallel Robot for Schönflies Motion Generation

2014 ◽  
Author(s):  
Shaoping Bai ◽  
Lasse Køgs Andersen ◽  
Carsten Rebbe Mølgaard
Keyword(s):  
Dynamic Performance ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Motion Generation ◽  
Stiffness Modeling ◽  
Pick And Place ◽  
Fea Simulation ◽  
Schönflies Motion ◽  
Pick And Place Operation ◽  
Good Agreement

This work deals with the design of parallel robots for the generation of pick-and-place operation, or Schönflies motion. The aim is to develop a robot with workspace optimized for fast pick-and-place operations, namely, a robot with a superellipsoidal reachable volume, which suits best for the pick-and-place operations on conveyers, where robots’ working areas are nearly rectangular. In this paper, the kinematics and stiffness modeling of the new robot are presented. A method of stiffness modeling by means of Castigliano’s Theorem is developed. Using the new method, the stiffness of the robot is analyzed. The results are compared with FEA simulation, which shows a good agreement between the results. The method is finally applied to the engineering design of the new robot for enhanced static and dynamic performance.

Singularity Analysis of a Plane-Symmetry 3-RPS Parallel Robot Based on Translational/Rotational Jacobian Matrices

2011 ◽  
Vol 121-126 ◽  
pp. 1590-1594
Author(s):  
Yan Shi ◽  
Hong Xin Yue ◽  
Yi Lu ◽  
Lian He Guo
Keyword(s):  
Jacobian Matrix ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
New Method ◽  
Plane Symmetry ◽  
Jacobian Matrices ◽  
Different Types

Firstly, 3-DOF parallel robots were classified into different types from the view of moving form. A new method of analyzing the singularity of 3-DOF parallel robots was introduced, which is based on translational Jacobian matrix and rotational Jacobian matrix. The singularity of parallel robots with pure translational form and pure rotational form was introduced summarily. Secondly, the process of solving the plane-symmetry 3-RPS parallel robot with combined moving forms was focused on, through which translational Jacobian matrix and rotational Jacobian matrix were adopted. Finally, the solving results were compared with the axis-symmetry 3-RPS parallel robot, which showed more general singularity can be solved through the new method.

scholarly journals Design and Analysis of a Novel Schönflies Motion Parallel Robot with Full Cycle Rotation

2021 ◽  
Author(s):  
Luquan Li ◽  
Yuefa Fang ◽  
Lin Wang ◽  
Jiaqiang Yao
Keyword(s):  
Complex Dynamics ◽  
Virtual Work ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
The Novel ◽  
Scara Robot ◽  
Pick And Place ◽  
Place Task ◽  
Schönflies Motion

Abstract Due to the complex structures of multi-limbed parallel robots, conventional parallel robots generally have limited workspace, complex kinematics, and complex dynamics, which increases the application difficulty of parallel robot in industrial engineering. To solve the above problems, this paper proposes a single-loop Schönflies motion parallel robot with full cycle rotation, the robot can generate Schönflies motion by the most simplified structure. The novel Schönflies motion parallel robot is a two-limb parallel mechanism with least links and joints, and each limb is driven by a 2-degree of freedom (DOF) cylindrical driver (C-driver). The full cycle rotation of the output link is achieved by “…R-H…” structure, where the revolute (R) and helical (H) joints are coaxial. Mobility, kinematics, workspace and singularity analysis of novel Schönflies motion parallel robot are analyzed. Then, dynamic model is formulated based on the principle of virtual work. Moreover, a pick-and-place task is implemented by proposed Schönflies motion parallel robot and a serial SCARA robot, respectively. The simulation results verify the correctness of the theoretical model. Furthermore, dynamics performances of Schönflies motion parallel robot and serial SCARA robot are compared, which reveal the performance merits of proposed Schönflies motion parallel robot.

scholarly journals Design of a Planar Cable-Driven Parallel Crane Without Parasitic Tilt

2021 ◽  
Author(s):  
Lionel Etienne ◽  
Philippe Cardou ◽  
Marceau Métillon ◽  
Stéphane Caro
Keyword(s):  
Total Mass ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Mobile Platform ◽  
Moving Platform ◽  
High Dynamics ◽  
Two Degree Of Freedom ◽  
High Payload

Abstract Cable-Driven Parallel Robots (CDPRs) offer high payload capacities, large translational workspace and high dynamics performances. Their rotational workspace is generally far more limited, however, which can be resolved by using cable loops, as was shown in previous research. In the case of fully-constrained CDPRs, cable loops can induce unwanted torques on the moving-platform, causing it to tilt and move away from its intended position, which we call parasitic tilt. Hence, the orientation accuracy of such robots is usually limited. This paper deals with the design, modelling and prototyping of a planar CDPR with infinite rotations, without parasitic tilt and without an additional motor. This robot, which we call a Cable-Driven Parallel Crane (CDPC), is composed of a mobile platform (MP) with an embedded mechanism and a transmission module. The MP is linked with the frame by a parallelogram of three cables to constrain its orientation, including a cable loop, as well as a fourth cable. The two-degree-of-freedom (dof) motions of the moving-platform of the CDPC and the internal dof of its embedded mechanism are actuated by a total of three actuators, which are fixed to the frame. As a consequence, the overall system is fully-actuated, its total mass and inertia in motion is reduced and it is free of parasitic tilts.

Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Jokin Aginaga ◽  
Xabier Iriarte ◽  
Aitor Plaza ◽  
Vicente Mata
Keyword(s):  
Vertical Plane ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Mobile Platform ◽  
Rehabilitation Robots ◽  
Knee Rehabilitation ◽  
Wide Range ◽  
Lower Mobility

Rehabilitation robots are increasingly being developed in order to be used by injured people to perform exercise and training. As these exercises do not need wide range movements, some parallel robots with lower mobility architecture can be an ideal solution for this purpose. This paper presents the design of a new four degree-of-freedom (DOF) parallel robot for knee rehabilitation. The required four DOFs are two translations in a vertical plane and two rotations, one of them around an axis perpendicular to the vertical plane and the other one with respect to a vector normal to the instantaneous orientation of the mobile platform. These four DOFs are reached by means of two RPRR limbs and two UPS limbs linked to an articulated mobile platform with an internal DOF. Kinematics of the new mechanism are solved and the direct Jacobian is calculated. A singularity analysis is carried out and the gained DOFs of the direct singularities are calculated. Some of the singularities can be avoided by selecting suitable values of the geometric parameters of the robot. Moreover, among the found singularities, one of them can be used in order to fold up the mechanism for its transportation. It is concluded that the proposed mechanism reaches the desired output movements in order to carry out rehabilitation maneuvers in a singularity-free portion of its workspace.

A Unified Approach to Direct Kinematics of Some Reduced Motion Parallel Manipulators

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
P. J. Zsombor-Murray ◽  
A. Gfrerrer
Keyword(s):  
Polynomial Solution ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Problem Solution ◽  
Unified Approach ◽  
Constraint Equations ◽  
Kinematic Models ◽  
Univariate Polynomial ◽  
Schönflies Motion ◽  
Direct Kinematics

After discussing the Study point transformation operator, a unified way to formulate kinematic problems, using “points moving on planes or spheres” constraint equations, is introduced. Application to the direct kinematics problem solution of a number of different parallel Schönflies motion robots is then developed. Certain not widely used but useful tools of algebraic geometry are explained and applied for this purpose. These constraints and tools are also applied to some special parallel robots called “double triangular” to show that the approach is flexible and universally pertinent to manipulator kinematics in reducing the complexity of some previously achieved solutions. Finally a novel two-legged Schönflies architecture is revealed to emphasize that good design is not only essential to good performance but also to easily solve kinematic models. In this example architecture, with double basally actuated legs so as to minimize moving mass, the univariate polynomial solution turns out to be simplest, i.e., of degree 2.

XR Quality Index: Evaluating RAN Transmission Quality for XR services over 5G and Beyond

2021 ◽  
Author(s):  
Shengyue Dou ◽  
Shuri Liao ◽  
Jian Wu ◽  
Kedi Wu ◽  
Erkai Chen ◽  
...  
Keyword(s):  
Quality Index ◽  
Transmission Quality
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