Abstract: A linear transformation, including a similarity model and an affine model, plays an important role in reference frame transformation problems. It establishes geometric relations between different reference frames by adopting ...

Abstract: The accurate determination of deflections of the vertical is a complex scientific task that can be time-consuming and expensive. On occasion, good approximations are required for surveying and engineering applications. ...

Abstract: The least-squares (LS) method is universally embraced to obtain approximate unique solutions and their statistics from overdetermined scientific experiments where the number of observations amply exceeds the number of ...

Abstract: New insights about the concept of local accuracies are elaborated in this article. Recently found evidence supports the mathematical rigor of equations previously published in this journal as a unique alternative to ...

Abstract: The correct form of Eq. (16) is as follows:Display FormulaR0r1c=LDR=e(1+n)[(2 fe−n−e−μπ/2t0/rd)(1+R)/2−4μ(1+2R)/[2(1+R)]]+e2n(1+R)/2−1

Abstract: This paper derives the surface geometry and machine tool settings for a double threaded variable pitch lead screw with four cylindrical meshing elements. A 4-axis machining center with a rotary ...

Abstract: This paper presents mathematical expressions for the surface geometry of variable pitch cylindrical cams with four conical meshing elements based on the theory of conjugate surfaces. The unit ...

Abstract: The objective of this case study is to evaluate the different approximations in the technical literature that are used to compute the variance-covariance matrix of local accuracies. This analysis compares the rigor and ...

Abstract: Civil infrastructure systems, such as harbors and airports, support transportation between international communities. Inspection of facilities in a large area is labor-intensive and time-consuming work, and the result can ...