scholarly journals A Closed Form Solution for the Self-Calibration of Heterogeneous Sensors

2012 ◽  
Author(s):  
Marco Crocco ◽  
Alessio Del Bue ◽  
Igor Barros Barbosa ◽  
Vittorio Murino
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Self ◽  
Heterogeneous Sensors ◽  
Self Calibration

Criterion for Preventing Self-Loosening of Preloaded Cap Screws Under Transverse Cyclic Excitation

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xianjie Yang ◽  
Sayed A. Nassar ◽  
Zhijun Wu
Keyword(s):  
Closed Form ◽  
Test Procedure ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Self ◽  
Experimental Setup ◽  
Transverse Loading ◽  
System Parameters ◽  
Transverse Excitation ◽  
Key Variables

In this paper, a novel criterion is developed for preventing the self-loosening of preloaded threaded cap screws under cyclic transverse loading. For a known cyclic excitation, the system parameters are used in the formulation of a closed form solution for the minimum fastener preload required for preventing self-loosening. The effect of several key variables is investigated; this includes bearing and thread friction coefficients, cap screw grip length, thread pitch, material, and cyclic amplitude of the transverse excitation. An experimental setup and test procedure are established. Comparison between the experimental and analytical clamp load variation results shows that the proposed criterion can accurately predict the requirements for preventing self-loosening.

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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