Direct kinematics of manipulators with hyper degrees of freedom and Frenet-Serret formula

2002 ◽  
Author(s):  
H. Mochiyama ◽  
E. Shimemura ◽  
H. Kobayashi
Keyword(s):  
Degrees Of Freedom ◽  
Direct Kinematics

The Kinematics of Spatial Double-Triangular Parallel Manipulators

1995 ◽  
Vol 117 (4) ◽  
pp. 658-661 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
J. Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Quaternion Algebra ◽  
Parallel Manipulators ◽  
Numerical Examples ◽  
Six Degrees Of Freedom ◽  
Dual Number ◽  
Direct Kinematics

Two versions of spatial double-triangular mechanisms are introduced, one with three and one with six degrees of freedom. Using dual-number quaternion algebra, a formula for the direct kinematics of these manipulators is derived. Numerical examples are included.

scholarly journals Modelamiento Cinemático Aproximado de un Prototipo de Robot Equino de 6 Grados de Libertad Para un Simulador de Tiro

2018 ◽  
Vol 3 (1) ◽  
pp. 532
Author(s):  
Jaime Eduardo Andrade Ramírez ◽  
Yeison Andrey Gómez Rubio ◽  
Diego Andrés Carranza Rivera
Keyword(s):  
Degrees Of Freedom ◽  
Robot Kinematics ◽  
Programming Environment ◽  
Control Software ◽  
Six Degrees Of Freedom ◽  
Psychological Injuries ◽  
Kinematic Study ◽  
Real Practice ◽  
Approximate Simulation ◽  
Direct Kinematics

This article shows the design, analysis and manufacturing of one equine robot prototype with six degrees of freedom along with the development and implementation of control software. This software has the purpose to drive and to calculate the robot kinematics. All of this allows studding the elements necessaries to make a simulator of shots for riders that can be used in education areas as a tool of didactic support in the courses in the police national of Colombia, ensuring that the riders do not suffer physical and psychological injuries during their formation and avoiding hurting the horses in the training of that courses. In addition, the riders can interact and experiment of safety way every situation that they could find in real practice. The system is based on the kinematic study according to the Denavit-Hartenberg algorithm, approximate simulation using Kinematic-ARM® and the mathematic medeling in the Matlab® programming environment. All tecniques give aproximate results of location of the manipulator tool.    Finally, it is possible to validate and analising the results comparing the practical and theoric values to determine the TCP error estimated in each movement.Keywords: Direct kinematics, equine robot, Denavit-Hartenberg (D-H), Degrees of Freedom (DOF), Tool Center Point (TCP).

scholarly journals Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 72 ◽  
Author(s):  
Stefan Schulz
Keyword(s):  
Lower Bound ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Mechanisms ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Measurement Units ◽  
Linear Actuators ◽  
Direct Kinematics

In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.

scholarly journals A Reconfigurable System Approach to the Direct Kinematics of a 5D.o.fRobotic Manipulator

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Diego F. Sánchez ◽  
Daniel M. Muñoz ◽  
Carlos H. Llanos ◽  
José M. Motta
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Dynamic Range ◽  
Hardware Acceleration ◽  
Hardware Architecture ◽  
Floating Point ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Transcendental Functions ◽  
Direct Kinematics

Hardware acceleration in high performance computer systems has a particular interest for many engineering and scientific applications in which a large number of arithmetic operations and transcendental functions must be computed. In this paper a hardware architecture for computing direct kinematics of robot manipulators with 5 degrees of freedom (5D.o.f) using floating-point arithmetic is presented for 32, 43, and 64 bit-width representations and it is implemented in Field Programmable Gate Arrays (FPGAs). The proposed architecture has been developed using several floating-point libraries for arithmetic and transcendental functions operators, allowing the designer to select (pre-synthesis) a suitable bit-width representation according to the accuracy and dynamic range, as well as the area, elapsed time and power consumption requirements of the application. Synthesis results demonstrate the effectiveness and high performance of the implemented cores on commercial FPGAs. Simulation results have been addressed in order to compute the Mean Square Error (MSE), using the Matlab as statistical estimator, validating the correct behavior of the implemented cores. Additionally, the processing time of the hardware architecture was compared with the same formulation implemented in software, using the PowerPC (FPGA embedded processor), demonstrating that the hardware architecture speeds-up by factor of 1298 the software implementation.

Direct and Inverse Kinematics for Coordinated Motion Tasks of a Two-Manipulator System

1996 ◽  
Vol 118 (4) ◽  
pp. 691-697 ◽  
Author(s):  
P. Chiacchio ◽  
S. Chiaverini ◽  
B. Siciliano
Keyword(s):  
Case Studies ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Coordinated Motion ◽  
Different Types ◽  
End Effectors ◽  
New Formulation ◽  
Direct Kinematics

A new formulation for direct kinematics of a system of two manipulators is presented This allows a straightforward description of general coordinated motion tasks in terms of meaningful absolute and relative variables An effective inverse kinematics algorithm is devised which exploits the above formulation where the task Jacobians are expressed in terms of the Jacobians of the single manipulators The scheme is extended to handle the presence of redundant degrees of freedom in the system Different types of grasp between the end effectors and a commonly held object are treated with minimum reformulation effort. Case studies are developed throughout the paper for a system of two PUMA 560 manipulators which illustrate the capabilities of the scheme.

scholarly journals Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control

2003 ◽  
Vol 125 (1) ◽  
pp. 33-42 ◽  
Author(s):  
N. Simaan ◽  
M. Shoham
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Geometric Interpretation ◽  
Parallel Robots ◽  
Redundant Robot ◽  
Moving Platforms ◽  
Stiffness Control ◽  
Derivatives Of ◽  
Direct Kinematics

This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms’ position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singularities of the active stiffness control. This geometric interpretation is utilized in an example of a planar 3 degrees-of-freedom redundant robot to determine its active stiffness control singularity.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

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