Dual quaternion-based inverse kinematics of the general spatial 7R mechanism

2008 ◽  
Vol 222 (8) ◽  
pp. 1593-1598 ◽  
Author(s):  
D Gan ◽  
Q Liao ◽  
S Wei ◽  
J S Dai ◽  
S Qiao
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Dual Quaternion ◽  
Whole Process ◽  
Inverse Kinematic Analysis ◽  
Angular Displacements ◽  
Output Equation ◽  
Theoretical Results

The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented. Dixon's resultant is used and the input—output equation is expressed in the form of a 6×6 determinant equated to zero, and the formulae to determine other angular displacements are expressed in the closed form. Numerical example confirms these theoretical results. The whole process is very simple and easy to program, which supplies a new method for the real use of the 7R mechanism.

Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 438-443 ◽  
Author(s):  
B. Padmanabhan ◽  
V. Arun ◽  
C. F. Reinholtz
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Variable Geometry ◽  
Inverse Kinematic Problem ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss

A variety of applications for variable-geometry truss manipulators (VGTMs) have been demonstrated or proposed in the literature. Most of these applications require solution to the inverse kinematic problem, yet only a few isolated examples of closed-form solution methods have been presented to date. This paper provides an overview to the general problem of inverse kinematic analysis of variable-geometry truss manipulators and presents new closed-form solution techniques for problems of practical importance.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

2013 ◽  
Vol 455 ◽  
pp. 533-538
Author(s):  
Edris Farah ◽  
Shao Gang Liu
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Surgical Robot ◽  
Decoupling Method ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

Design and Construction of a Statically-Balanced Direct Drive ARM

1987 ◽  
Author(s):  
H. Kazerooni ◽  
S. Kim
Keyword(s):  
Closed Form ◽  
Robot Manipulator ◽  
Impedance Control ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Direct Drive ◽  
University Of Minnesota ◽  
Closed Form Solutions ◽  
The University

Abstract A statically-balanced direct drive robot manipulator is being constructed at the University of Minnesota for analysis of manufacturing tasks such as deburrlng and grinding when Impedance Control (8, 10, 11) is used to control the robot. This mechanism using a four bar linkage is designed without extra counterweights. As a result of elimination of the gravity forces on the drive system, smaller actuators (and consequently smaller amplifiers) are chosen to guarantee the acceleration of about 5g without overheating the motors. This mechanism results in closed-form solution for Inverse kinematics. The closed-form solutions for dynamic and Inverse kinematic have been derived. High torque, low speed brush-less AC synchronous motors are used to power the robot. The relatively “large” workspace of this configuration is suitable for manufacturing tasks. Graphite epoxy composite material is being used for the construction of the robot links.

Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures

1992 ◽  
Vol 114 (1) ◽  
pp. 68-73 ◽  
Author(s):  
V. Parenti-Castelli ◽  
C. Innocenti
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
Forward Displacement ◽  
Form Analysis ◽  
Displacement Analysis ◽  
Theoretical Results ◽  
Forward Displacement Analysis

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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