Configuration Spaces of Spatial Linkages

2015 ◽  
Author(s):  
D Blanc ◽  
N Shvalb
Keyword(s):  
Configuration Spaces ◽  
Spatial Linkages

scholarly journals Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

Configuration spaces of n lines in affine (n + k)-space

2007 ◽  
Vol 146 (1) ◽  
pp. 5474-5482
Author(s):  
Margareta Boege ◽  
Luis Montejano
Keyword(s):  
Configuration Spaces

Discrete positions method in kinematics and control of spatial linkages

1980 ◽  
Vol 15 (1) ◽  
pp. 47-60 ◽  
Author(s):  
M.S Konstantinov ◽  
M.D Markov
Keyword(s):  
Spatial Linkages ◽  
And Control

Collision-Free Motion Planning for an Aligned Multiple-turret System Operating in Extreme Environment

Robotica ◽  
2021 ◽  
pp. 1-30
Author(s):  
Ümit Yerlikaya ◽  
R.Tuna Balkan
Keyword(s):  
Path Planning ◽  
Extreme Environment ◽  
Configuration Spaces ◽  
Planning Problem ◽  
Different Types ◽  
Planning Algorithm ◽  
Line Path ◽  
Path Planning Algorithm ◽  
Path Planning Problem ◽  
System Operating

Abstract Instead of using the tedious process of manual positioning, an off-line path planning algorithm has been developed for military turrets to improve their accuracy and efficiency. In the scope of this research, an algorithm is proposed to search a path in three different types of configuration spaces which are rectangular-, circular-, and torus-shaped by providing three converging options named as fast, medium, and optimum depending on the application. With the help of the proposed algorithm, 4-dimensional (D) path planning problem was realized as 2-D + 2-D by using six sequences and their options. The results obtained were simulated and no collision was observed between any bodies in these three options.

Efficient Dynamic Computer Simulation of Simple-Closed Spatial Linkages

1990 ◽  
Author(s):  
L. T. Wang
Keyword(s):  
Computer Simulation ◽  
Computational Algorithm ◽  
Equations Of Motion ◽  
Joint Space ◽  
Kinematic Chains ◽  
Spatial Linkages ◽  
Dynamic Computer Simulation ◽  
The Stability ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.

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