A New and Efficient Algorithm for the Inverse Kinematics of a General Serial 6R

2005 ◽  
Author(s):  
Manfred L. Husty ◽  
Martin Pfurner ◽  
Hans-Peter Schro¨cker
Keyword(s):  
Efficient Algorithm ◽  
Inverse Kinematics ◽  
Linear Equations ◽  
Main Idea ◽  
Kinematic Chain ◽  
Joint Angles ◽  
Degree Polynomial ◽  
Geometric Information ◽  
Multidimensional Geometry ◽  
Dimensional Projective Space

In this paper a new and very efficient algorithm to compute the inverse kinematics of a general 6R serial kinematic chain is presented. The main idea is to make use of classical multidimensional geometry to structure the problem and to use the geometric information before starting the elimination process. For the geometric preprocessing we use the Study model of Euclidean displacements, sometimes called kinematic image, which identifies a displacement with a point on a six dimensional quadric S62 in seven dimensional projective space P7. The 6R chain is broken up in the middle to form two open 3R chains. The kinematic image of a 3R chain turns out to be a Segre-manifold consisting of a one parameter set of 3-spaces. The intersection of two Segre-manifolds and S62 yields 16 points which are the kinematic images representing the 16 solutions of the inverse kinematics. Algebraically this procedure means that we have to solve a system of seven linear equations and one resultant to arrive at the univariate 16 degree polynomial. From this step in the algorithm we get two out of the six joint angles and the remaining 4 angles are obtained straight forward by solving the inverse kinematics of two 2R chains.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

scholarly journals Exclusive Reconstruction ofB-Decays with Missing Neutrals

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
M. Dima
Keyword(s):  
Main Idea ◽  
Single Track ◽  
Theoretical Interest ◽  
Geometric Information ◽  
Decay Channels

Often decay channels that are of theoretical interest cannot be reconstructed exclusively due to missing neutrals (such as neutrinos), or due to single-track vertices. This situation appears both in underground astrophysics experiments as well as in conventional accelerator experiments. A method to “recover” such missing particles from their kinematics and reconstruct “exclusively” the modes would benefit both domains in a number of ways. The main idea is to combine 4-momentum conservations in vertices with available geometric information in the event. The paper gives details of such methods on theBs0→Ds−K+,Ds−→K+K−π−(π0)prototype decay, which also encounters 2-fold ambiguities in its solutions. Such ambiguities can be lifted and the paper shows how, while also addressing the potential the method has in physics analyses and detector studies.

scholarly journals A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Fernando Gonçalves ◽  
Tiago Ribeiro ◽  
António Fernando Ribeiro ◽  
Gil Lopes ◽  
Paulo Flores
Keyword(s):  
Recursive Algorithm ◽  
Kinematic Chain ◽  
Robotic Systems ◽  
Mobile Manipulator ◽  
Euler Angles ◽  
Joint Angles ◽  
Main Research ◽  
Kinematic Chains ◽  
Research Fields ◽  
Forward Kinematic

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

An Efficient Algorithm for Finding Optimum Code Under the Condition of Incident Degree

1992 ◽  
Author(s):  
T. J. Jongsma ◽  
W. Zhang
Keyword(s):  
Computer Program ◽  
Efficient Algorithm ◽  
Kinematic Chain ◽  
Isomorphism Problem ◽  
Kinematic Chains ◽  
Adjacency Matrices ◽  
Set Up

Abstract This paper deals with the identification of kinematic chains. A kinematic chain can be represented by a weighed graph. The identification of kinematic chains is thereby transformed into the isomorphism problem of graph. When a computer program has to detect isomorphism between two graphs, the first step is to set up the corresponding connectivity matrices for each graph, which are adjacency matrices when considering adjacent vertices and the weighed edges between them. Because these adjacency matrices are dependent of the initial labelling, one can not conclude that the graphs differ when these matrices differ. The isomorphism problem needs an algorithm which is independent of the initial labelling. This paper provides such an algorithm.

A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator

2007 ◽  
Vol 42 (1) ◽  
pp. 66-81 ◽  
Author(s):  
Manfred L. Husty ◽  
Martin Pfurner ◽  
Hans-Peter Schröcker
Keyword(s):  
Efficient Algorithm ◽  
Inverse Kinematics

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

2005 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

A Fuzzy Algorithm to Study the Inverse Kinematics Problem of a Serial Manipulator

2015 ◽  
Vol 783 ◽  
pp. 77-82
Author(s):  
Francesco Aggogeri ◽  
Nicola Pellegrini ◽  
Riccardo Adamini
Keyword(s):  
Inverse Kinematics ◽  
Linear Equations ◽  
Rigid Bodies ◽  
Robust Performance ◽  
Serial Chain ◽  
Interactive Algorithm ◽  
Inverse Kinematics Problem ◽  
Transcendental Functions ◽  
Computationally Expensive ◽  
Non Linear Equations

This paper presents a fuzzy logic to solve the inverse kinematics problem. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having transcendental functions are difficult and computationally expensive. This study focuses on a serial manipulator modelled as a serial chain of rigid bodies connected by joints. A new fuzzy interactive algorithm is developed and the effectiveness is compared with other methods on a SCARA robot. It converge in all the developed simulations showing a robust performance.

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