Efficient Closed-Form Solution of the Kinematics of a Tunnel Digging Machine

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Paolo Boscariol ◽  
Alessandro Gasparetto ◽  
Lorenzo Scalera ◽  
Renato Vidoni
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
Large Size ◽  
Closure Equation ◽  
Class 1 ◽  
Spherical Mechanism ◽  
Kinematic Solution

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

Structure design and kinematics of a robot manipulator

Robotica ◽  
1988 ◽  
Vol 6 (4) ◽  
pp. 299-309 ◽  
Author(s):  
Kesheng Wang ◽  
Terje K. Lien
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Structure Design ◽  
General Algorithm ◽  
6 Degrees Of Freedom

SUMMARYIn this paper we show that a robot manipulator with 6 degrees of freedom can be separated into two parts: arm with the first three joints for major positioning and wrist with the last three joints for major orienting. We propose 5 arms and 2 wrists as basic construction for commercially robot manipulators. This kind of simplification can lead to a general algorithm of inverse kinematics for the corresponding configuration of different combinations of arm and wrist. The approaches for numerical solution and closed form solution presented in this paper are very efficient and easy for calculating the inverse kinematics of robot manipulator.

scholarly journals Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
M.-C. Casabán ◽  
J.-C. Cortés ◽  
B. García-Mora ◽  
L. Jódar
Keyword(s):  
Stochastic Process ◽  
Temperature Distribution ◽  
Numerical Solution ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mean Square ◽  
Random Boundary ◽  
Numerical Examples

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.

scholarly journals Average trapping time on weighted directed Koch network

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Zikai Wu ◽  
Yu Gao
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Numerical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Trapping Time ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks

Abstract Numerous recent studies have focused on random walks on undirected binary scale-free networks. However, random walks with a given target node on weighted directed networks remain less understood. In this paper, we first introduce directed weighted Koch networks, in which any pair of nodes is linked by two edges with opposite directions, and weights of edges are controlled by a parameter θ . Then, to evaluate the transportation efficiency of random walk, we derive an exact solution for the average trapping time (ATT), which agrees well with the corresponding numerical solution. We show that leading behaviour of ATT is function of the weight parameter θ and that the ATT can grow sub-linearly, linearly and super-linearly with varying θ . Finally, we introduce a delay parameter p to modify the transition probability of random walk, and provide a closed-form solution for ATT, which still coincides with numerical solution. We show that in the closed-form solution, the delay parameter p can change the coefficient of ATT, but cannot change the leading behavior. We also show that desired ATT or trapping efficiency can be obtained by setting appropriate weight parameter and delay parameter simultaneously. Thereby, this work advance the understanding of random walks on directed weighted scale-free networks.

scholarly journals Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Gian Luigi Gragnani ◽  
Maurizio Diaz Mendez
Keyword(s):  
Closed Form ◽  
Cross Sections ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Computation Time ◽  
Shape Reconstruction ◽  
Form Solution ◽  
Scattering Data ◽  
Equivalent Sources ◽  
Value Decomposition

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time.

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

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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