Geometrical Kinematic Analysis of a Planar Serial Manipulator Using a Barycentric Formula

2015 ◽  
Author(s):  
Chan Lee ◽  
Jeh Won Lee ◽  
TaeWon Seo
Keyword(s):  
Numerical Method ◽  
Kinematic Analysis ◽  
Screw Theory ◽  
Geometric Analysis ◽  
Geometric Interpretation ◽  
Trial And Error ◽  
Geometrical Meaning ◽  
The Past ◽  
Perpendicular Distance ◽  
Barycentric Formula

The kinematics, instantaneous motion, and statics of a manipulator have recently been determined algebraically. In the past, such studies did not provide any intuition about the equation. Robot designers had to use a numerical method or trial-and-error solver with unintuitive equations. Alternatively, all algebraic processes have their own geometrical meaning. Geometric analysis provides intuition for designing the linkages of a robot. Screw theory and barycentric formulas are used to find meaningful geometric measures. The kinematics and statics of a manipulator are described by an axis screw and its reciprocal line screw. The barycenter of a triangle with edges and a perpendicular distance between the two screws are useful geometric measures for geometric analysis. This study provides a geometric interpretation of the kinematics and statics of a planar manipulator using a barycentric formula.

Brains as Engines of Association

2019 ◽  
Author(s):  
Dale Purves
Keyword(s):  
Neural Systems ◽  
Neural Function ◽  
Trial And Error ◽  
Nervous Systems ◽  
The Past ◽  
Sensing Systems ◽  
Lifetime Experience ◽  
Survival And Reproduction ◽  
Pros And Cons ◽  
And Behavior

Brains as Engines of Association seeks an operating principle of the human brain and is divided into four parts. The first part (“What Nervous Systems Do for Animals”) is intended to set the stage for understanding the emergence of neural systems as promoting what all organisms must accomplish: survival and reproduction. The second part (“Neural Systems as Engines of Association”) lays out the general argument that biological sensing systems face a daunting problem: they cannot measure the parameters of the world in the way physical instruments can. As a result, nervous systems must make and update associations (synaptic connections) on the basis of empirical success or failure over both evolutionary and individual time. The third part (“Evidence that Neural Systems Operate Empirically”) reviews evidence accumulated over the past 20 years that supports this interpretation in vision and audition, the sensory systems that have been most studied from this or any other perspective. Finally, the fourth part (“Alternative Concepts of Neural Function”) considers the pros and cons of other interpretations of how brains operate. The overarching theme is that the nervous systems of humans and every other animal operate on the basis associations between stimuli and behavior made by trial and error over species and lifetime experience.

Kinematics of Meshing Surfaces Using Geometric Algebra

2003 ◽  
Author(s):  
Scott M. Miller
Keyword(s):  
Geometric Algebra ◽  
Screw Theory ◽  
Three Dimensional ◽  
Normal Vector ◽  
The Past ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
The Common ◽  
Two Bodies ◽  
Theoretical Developments

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

Kinematic calibration of serial robot using dual quaternions

2019 ◽  
Vol 46 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Guozhi Li ◽  
Fuhai Zhang ◽  
Yili Fu ◽  
Shuguo Wang
Keyword(s):  
Kinematic Analysis ◽  
Quaternion Algebra ◽  
Error Model ◽  
Kinematic Calibration ◽  
Dual Quaternion ◽  
Robot Calibration ◽  
Geometrical Meaning ◽  
Content Type ◽  
Dual Quaternions ◽  
Serial Robot

Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe. Findings Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC. Originality/value The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

Dimensional Synthesis of a Novel 2T2R Parallel Manipulator for Medical Applications

2014 ◽  
Author(s):  
Nitish Kumar ◽  
Olivier Piccin ◽  
Bernard Bayle
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Structural Parameters ◽  
Geometric Analysis ◽  
Medical Applications ◽  
Dimensional Synthesis ◽  
Synthesis Algorithm ◽  
Percutaneous Procedures ◽  
Actuated Joints

This paper deals with the dimensional synthesis of a novel parallel manipulator for medical applications. This parallel mechanism has a novel 2T2R mobility derived from the targeted application of needle manipulation. The kinematic design of this 2T2R manipulator and its novelty are illustrated in relation to the percutaneous procedures. Due to the demanding constraints on its size and compactness, achieving a large workspace especially in orientation, is a rather difficult task. The workspace size and kinematic constraint analysis are considered for the dimensional synthesis of this 2T2R parallel mechanism. A dimensional synthesis algorithm based on the screw theory and the geometric analysis of the singularities is described. This algorithm also helps to eliminate the existence of voids inside the workspace. The selection of the actuated joints is validated. Finally, the dimensions of the structural parameters of the mechanism are calculated for achieving the required workspace within the design constraints of size, compactness and a preliminary prototype without actuators is presented.

Random Collocation Method (RCM)

2010 ◽  
Author(s):  
Hiroshi Isshiki
Keyword(s):  
Numerical Method ◽  
Collocation Method ◽  
Analytical Method ◽  
Traditional Method ◽  
Analytical Approach ◽  
Numerical Procedure ◽  
Computational Method ◽  
Weak Point ◽  
The Past ◽  
Innovative Idea

Recently, young people’s concern on theory is becoming very poor. If there is a numerical procedure that is friendlier with theory, the distance between theory and calculation would be decreased much, and the interaction between them would become more active. When the geometry of the domain is simple, the traditional analytical method using function expansion is very convenient in many numerical problems. In many problems, it has given very useful solutions for various problems. However, its effectiveness is usually limited to simple geometries of the domain. In the past, a fusion of the analytical approach and computational one has not been pursued sufficiently. If it becomes possible, it may give a different paradigm for obtaining the numerical solution. In the present paper, an innovative idea named Random Collocation Method (RCM) is discussed on how to overcome the weak point of the traditional method by combining it with computational method. It is the purpose of the present paper to develop the simplest numerical method and to make the distance between the theory and numerical method as small as possible.

Plastic and reconstructive surgery

2016 ◽  
Keyword(s):  
Randomized Controlled Trials ◽  
Plastic Surgery ◽  
Reconstructive Surgery ◽  
Controlled Trials ◽  
Evidence Based ◽  
Trial And Error ◽  
Plastic And Reconstructive Surgery ◽  
Randomized Controlled ◽  
The Past ◽  
Evidence Based Surgery

In plastic and reconstructive surgery, innovation and creativity have been foremost, with science and evidence following. Unlike for a number of other specialties, the advances in plastic surgery have largely come from imagination, innovations, and trial and error, rather than from scientific trials. Somewhat more than for the rest of surgery, in plastics (where the art and craft of each particular surgeon counts immeasurably), randomized controlled trials of techniques have failed to be generated in the past, due to the difficulty of objectively assessing the success of surgery with an aesthetic-based nature. Consequently, evidence-based study of plastic surgery is a relatively new and developing field. This chapter focuses on the growing importance of evidence-based surgery in this specialty, showing that scientific trials are now being performed with increasing frequency.

Position and Orientation Characteristic Equation for Topological Design of Parallel Mechanisms

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Output Link ◽  
Geometrical Meaning ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure of parallel mechanism and position and orientation characteristic (in short, POC) of its motion output link. It deals with: (1) The symbolic representation and the invariant of topological structure of mechanism; (2) The matrix representation of POC of motion output link; (3) The POC equations of parallel mechanism and its symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules, and has clear geometrical meaning. So, it is easy to use. The forward operation of the POC equations can be used for structural analysis; its inverse operation can be used for structural synthesis. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup.

Deep Drawing Height Analysis of Rectangular Cup Drawing

2010 ◽  
Author(s):  
Francisco J. Colorado Alonso ◽  
Hugo I. Medelli´n Castillo ◽  
Pedro de J. Garci´a Zugasti ◽  
Dirk F. de Lange
Keyword(s):  
Deep Drawing ◽  
Theoretical Expression ◽  
Drawing Process ◽  
Trial And Error ◽  
Contact Conditions ◽  
Deep Drawing Process ◽  
The Past ◽  
Theoretical And Numerical Analysis ◽  
Cylindrical Cup ◽  
Cup Drawing

The deep drawing process is widely used in industry because it allows the production of parts with reduced weight and good mechanical properties. However, the deep drawing process of non-cylindrical shapes still relies on experimental and trial and error methods, leading to high costs and long development times. The deformation mechanism of non-cylindrical cup drawing is theoretically very complex because of the large elasto-plastic stress and strain, and contact conditions between the tools and the sheet metal involved. In particular, several attempts have been tried in the past to perform theoretical and numerical analysis of rectangular cups. This paper presents an analysis of the allowable deep drawing height (DDH) of rectangular cups. The aim of this paper is twofold: 1) to analyze and estimate the allowable DDH of rectangular parts using theoretical, numerical (FEM) and experimental methods, and 2) identify the theoretical expression that predicts with the highest accuracy the allowable DDH of rectangular parts. A new theoretical expression for predicting this DDH is also proposed. To perform the study FEM is used together with the experimental data from industrial parts. The results show the accuracy of each theoretical expression in predicting the allowable DDH of rectangular parts.

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