Calculation of the unit normal vector using the cross-curve moving mask method for probe radius compensation of a freeform surface measurement

Measurement ◽  
2010 ◽  
Vol 43 (4) ◽  
pp. 469-478 ◽  
Author(s):  
Ruey-Tsung Lee ◽  
Fang-Jung Shiou
2013 ◽  
Vol 332 ◽  
pp. 405-410 ◽  
Author(s):  
Erzsebet Faluvegi ◽  
Luciana Cristea

First of all, using the coordinate measuring machines 3D measured points are acquired. These machines are widely used in gear manufacturing industry but each of them handles the compensation problem in different ways. Thus, the aim of this paper is to compensate the measured data points on the tooth surface of bevel gears with the value of probe radius. This paper presents an option to solve the compensation with the value of probe radius and shows the steps, the methodology to implement this idea in practical use. There are used triangular meshes on the measured data points and determined the normal vector of each point detected on the tooth surface of the bevel gears.


2021 ◽  
Author(s):  
Xiaokai Yang ◽  
Qiancheng Yang ◽  
Zhaobang Liu

Abstract To discusses and analyzes how to realize the design of posterior semicircular canal BPPV diagnostic maneuver. First, measure the spatial attitude of the human semicircular canal, establish a BPPV virtual simulation platform, then analyze the key positions of the maneuver, and finally design a new diagnostic maneuver according to the demand, and perform physical simulation verification. The average value of the unit normal vector of the right posterior semicircular plane is [ 0.660, 0.702, 0.266], after rotate -46.8 ° around Z axis and 15.4 ° around Y axis, it parallel to the X axis. After that, when the tilt back angle reaches 70 °, the free otoconia in the left utricle will fall into the common crus; when bend forward 53.3°, the unit normal vector of the crista ampullaris plane of the posterior semicircular canal to the XY plane; when bend forward angle reaches 30°, the otoconia slides to the opening of the ampulla; when bend forward angle reaches 70°, the otoconia slides to the bottom of the crista ampullaris. The shallow pitching Yang maneuver is designed as turn head 45° to the one side, bend forward 45°, tilt back 90°, and bend forward 90°. The deep pitching Yang maneuver is designed as bend forward 90°, turn head 45° to one side, tilt back 135°, and bend forward 90°. A new posterior semicircular BPPV diagnostic test is designed to make the induced nystagmus have the characteristics of long latency, reversal, and repeatability, will not cause the inhibitory stimulation of the contralateral superior semicircular canal, and has good operation fault tolerance, which is of great value for clinical and scientific research.


Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos

This chapter consists mainly of definitions and various properties (without proofs) of spaces and operators used in this book. It defines O as an open set in Rᶰ such that it is locally on one side of its boundary Γ‎ := δ‎O, which is supposed to be bounded and Lipschitz. The chapter is mainly focused on the case of N = 3. Further, without loss of generality, the chapter supposes that Γ‎ is connected (for otherwise, one could work separately at each connected component). Such a set O is referred to as ‘regular’ in what follows. Let n denote the outward unit normal vector to Γ‎. In addition, let Oₑ := Rᶰ∖Ō: By N₀ we denote the set N ∪ {0}.


2017 ◽  
Vol 35 (3) ◽  
pp. 79-93
Author(s):  
Tugba Mert ◽  
Baki Karlıga

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.


2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Roland Duduchava ◽  
Eugene Shargorodsky ◽  
George Tephnadze

AbstractIn many applications it is important to be able to extend the (outer) unit normal vector field from a hypersurface to its neighborhood in such a way that the result is a unit gradient field. The aim of this paper is to provide an elementary proof of the existence and uniqueness of such an extension.


Author(s):  
S-T Chiou ◽  
J-C Tzou

It is proved in this paper that the hodograph of a frequency term (for example the kth frequency term) of the shaking force of spatial mechanisms is an ellipse. Furthermore, expressions are provided for the lengths and attitudes of the semi-axes of this ellipse in terms of Fourier coefficients of the shaking force. Accordingly, a pair of counterweights, contra-rotating at k times of cycle frequency with their axes parallel to the unit normal vector of the hodograph plane, can be installed for eliminating the frequency term of the shaking force of spatial mechanisms. An example of a seven-link 7-R spatial linkage is included.


2020 ◽  
Vol 199 ◽  
pp. 104422
Author(s):  
Li Min ◽  
Huang Jingcong ◽  
Zhang Yang ◽  
Wang Yuan ◽  
Wu Changsong ◽  
...  

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