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.

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.

scholarly journals Inverse kinematics for the variable geometry truss manipulator via a Lagrangian dual method

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141666677 ◽  
Author(s):  
Yanchun Zhao ◽  
Shiqiang Hu ◽  
Yongsheng Yang
Keyword(s):  
Inverse Kinematics ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Variable Geometry ◽  
Quadratic Constraints ◽  
Fixed Base ◽  
Inverse Kinematics Problem ◽  
Central Curve ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

This article studies the inverse kinematics problem of the variable geometry truss manipulator. The problem is cast as an optimization process which can be divided into two steps. Firstly, according to the information about the location of the end effector and fixed base, an optimal center curve and the corresponding distribution of the intermediate platforms along this center line are generated. This procedure is implemented by solving a non-convex optimization problem that has a quadratic objective function subject to quadratic constraints. Then, in accordance with the distribution of the intermediate platforms along the optimal center curve, all lengths of the actuators are calculated via the inverse kinematics of each variable geometry truss module. Hence, the approach that we present is an optimization procedure that attempts to generate the optimal intermediate platform distribution along the optimal central curve, while the performance index and kinematic constraints are satisfied. By using the Lagrangian duality theory, a closed-form optimal solution of the original optimization is given. The numerical simulation substantiates the effectiveness of the introduced approach.

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.

A New Algorithm for a Spatial Serial Robot

2010 ◽  
Vol 29-32 ◽  
pp. 952-955
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Duan Ling Li
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Greatest Common Divisor ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Serial Robot ◽  
Univariate Polynomial

In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.

scholarly journals Inverse kinematics of asymmetric octahedral variable geometry truss manipulator with obstacle avoidance through inexact interior point optimization

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881718
Author(s):  
Yanchun Zhao ◽  
Shiqiang Hu ◽  
Yongsheng Yang
Keyword(s):  
Obstacle Avoidance ◽  
Interior Point ◽  
Inverse Kinematics ◽  
Sparse Matrix ◽  
Operation Time ◽  
Variable Geometry ◽  
Quadratic Constraints ◽  
Memory Space ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

This article studies the inverse kinematics for asymmetric octahedral variable geometry truss manipulator with obstacle avoidance. The inverse kinematics problem is cast as a nonconvex optimization that having quadratic objective function subject to quadratic constraints. This article uses an inexact interior point optimization to solve it, which is developed on the basis of the imprecise algorithm Ipopt. According to the particularity of our actual optimization problem, each iteration undergoes specific modifications so as to minimize the memory consumption as well as computation time. Utilizing the sparse and binary characteristics of the coefficient matrix, respectively, the algorithm allocates the computation to the finite sparse matrix vector multiplication and changes the storage form, which greatly reduces the memory space. Based on the unique rules of inverse kinematics, the iteration direction of the algorithm becomes more clear. With the aid of mechanical constraints inherent in the manipulator, the algorithm omits the feasibility recovery part that embedded in the solver Ipopt. All these make us save the operation time greatly while utilizing Ipopt algorithm. To demonstrate the effectiveness of the proposed approach, the scheme was applied to obstacle avoidance inverse kinematics of variable geometry truss manipulator with three modules.

Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

2011 ◽  
Vol 143-144 ◽  
pp. 265-268
Author(s):  
Zhi Zhong Liu ◽  
Hong Yi Liu ◽  
Zhong Luo
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Kinematics Analysis ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Joint Method

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

Kinematics of a 4-DOF Bipod Parallel Grinder

2006 ◽  
Vol 304-305 ◽  
pp. 431-435
Author(s):  
Ping Zou ◽  
J. Angeles
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Horizontal Plane ◽  
Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Moving Platform ◽  
Forward And Inverse Kinematics

In this paper, a novel bipod parallel grinder with four controlled degrees of freedom is introduced. The moving platform of this 2-leg parallel grinder can always keep moving in horizontal plane by means of four-parallelogram mechanism (Π joints). The closed-form solutions of forward and inverse kinematics are derived.

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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