Closed-Form Inverse Kinematic Solution of Triple Octahedron Variable Geometry Truss Manipulators

1998 ◽  
Author(s):  
Li Ju Xu ◽  
Yang Duan ◽  
Sui Xian Yang
Keyword(s):  
Closed Form ◽  
Solution Procedure ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Output Variable ◽  
Output Displacement ◽  
Displacement Equation ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss ◽  
Kinematic Solution

Abstract In this paper the triple-octahedron variable geometry truss manipulator is presented and its inverse displacement analysis in closed form is studied, Input-output displacement equation in one output variable is derived. The solution procedure is given in detail. A numerical example is presented for illustration.

scholarly journals Inverse kinematic analysis for triple-octahedron variable-geometry truss manipulators

2001 ◽  
Vol 215 (2) ◽  
pp. 247-251 ◽  
Author(s):  
L J Xu ◽  
G Y Tian ◽  
Y Duan ◽  
S X Yang
Keyword(s):  
Solution Procedure ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Input Output ◽  
Output Variable ◽  
Output Displacement ◽  
Displacement Equation ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

In this paper, a new triple-octahedron variable-geometry truss manipulator is presented. Its inverse kinematic solutions in closed form are studied. An input-output displacement equation in one output variable is derived. The solution procedure is given in detail. A numerical example is illustrated.

The Inverse Kinematic Solution of the Tetrahedron Based Variable-Geometry Truss Manipulator

1992 ◽  
Vol 114 (3) ◽  
pp. 433-437 ◽  
Author(s):  
M. Subramaniam ◽  
S. N. Kramer
Keyword(s):  
Analytic Solution ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Joint Angles ◽  
Serial Link ◽  
Revolute Joints ◽  
Order Polynomial ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss ◽  
Kinematic Solution

The Tetrahedron Based Variable Geometry Truss Manipulator is comprised of a series of tetrahedrons stacked upon one another in a spiraling manner. When one link of each “cell” is made variable in length, the system can be effectively used as a remote manipulator. The manipulator is kinematically equivalent to a serial link manipulator consisting only of revolute joints where the angle between successive axes is 120°. In this paper, a closed-form analytic solution for the six-celled (6R series) variable geometry truss manipulator is obtained. It is shown that a sixteenth order polynomial in one of the joint angles is found which leads to at most sixteen solutions.

Forward and Inverse Kinematic Solution of the Variable Geometry Truss Robot Based on an N-Celled Tetrahedron-Tetrahedron Truss

1990 ◽  
Vol 112 (1) ◽  
pp. 16-22 ◽  
Author(s):  
S. Jain ◽  
S. N. Kramer
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Load Carrying ◽  
Forward And Inverse Kinematics ◽  
Actuation Scheme ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss ◽  
Exceptional Stability ◽  
Kinematic Solution

The Tetrahedron-Tetrahedron truss (or TT truss for short) has exceptional stability, stiffness, and load-carrying capabilities. Because of this fact, the TT truss is well suited for use as a variable geometry truss manipulator (VGTM) by appropriately choosing certain links whose variable lengths can be controlled. Since the TT truss is composed of n-cells, its applications include the retrieval of equipment, bridges over and around obstacles, and applications which utilize collapsible programmable structures capable of relatively large displacements. In this paper an actuation scheme and the general solution to the forward and inverse kinematics problems for an n-celled TT truss are presented. Numerical examples are also presented.

A Direct Displacement Solution to the Dodecahedron Variable Geometry Truss Manipulator

1996 ◽  
Author(s):  
Li-Ju Xu ◽  
Sui-Xian Yang ◽  
Zhao-Fei Zhou
Keyword(s):  
Solution Procedure ◽  
Homotopy Continuation ◽  
Variable Geometry ◽  
Numerical Example ◽  
Position Problem ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

Abstract Homotopy continuation algorithms for solving the direct position problem of the dodecahedron variable geometry truss manipulator are proposed in this paper. The homogeneous equations and the division of groups are presented which give the lowest Bezout number. The solution procedure is given in detail. A numerical example is presented for illustration.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

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.

Analytical Model Method for Dynamics of N-Celled Tetrahedron-Tetrahedron Variable Geometry Truss Manipulators

1998 ◽  
Author(s):  
Li Ju Xu ◽  
Hong Li ◽  
Shou Wen Fan
Keyword(s):  
Analytical Model ◽  
Variable Geometry ◽  
Symbolic Form ◽  
Model Method ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

Abstract In this paper some fundamental formulae are derived for tetrahedron-based variable geometry truss manipulator which is composed of a series of tetrahedrons stacked upon each other such that one link in each cell is made variable on length. Analytical model for dynamics of the manipulator is established, and expressions in numeric-symbolic form of model matrices are derived. An example is given for illustration.

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