• Journal of the Korean Society for Precision Engineering
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• v.11 no.5
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• pp.88-97
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• 1994

We persent a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic parameters in the POE formula vary smoothly with changes in the joint axes;ad hoc methods designed to address the inherent singularities in the D-H parameters are therefore are therefore unnecessary. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms. Simulation results with a 6-axis open chain are presented.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.337-348
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• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.357-370
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• 2000

In [6], Cheng-Ye You gave a condition equivalent to the Nielsen number product formula for fiber maps. And Jerzy Jezierski also gave a similar condition for coincidences of fiber maps. The main purpose of this paper is to find the condition for which holds the product formula for Nielsen root numbers N(f;a) = N(f;a) N(fb;a).

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.94-97
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• 1999

The study has been performed for the relation between die and product in closed die upsetting by the experiment. the strain of die has been given by the simple experiment using the strain gauge located at the outer surface of die and the deformation history of die and product has been given by the experiment and Lame's formula. the product with accurate dimension and shape can be obtained by analysing elastic deformation of die during upsetting process. The deformation of die during metal forming process has been given by the experiment and lame's formula. The product with accurate dimension and shape can be obtained by analysing elastic deformation of die during upsetting process. The deformation of die during metal forming process has been usually predicted by the experience of industrial engineers of finite element analysis. But it is difficult to predict the dimension of product at unloading and ejected states. The study has given useful result for the deformation history of die and product through the experiment and Lame's formula at closed die upsetting and can be applied in the die design for product with accurate dimension.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.83-87
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• 2000

The die for cold forging gets a ver high axial load and radial pressure during processing and hence deforms considerably in the radial direction. This radial deformation of die becomes a important factor influencing the dimensional accuracy of a product. In order to obtain a product with highly accurate dimension therefore it is essential to acquire some information on elastic deformation of the die and the product. The study has been performed for the relation of the deformation between a die and a product in backward extrusion. The strain of the die has been given by the simple experiment using the strain gauges attached to the outer surface of the die. Also the history of the deformation of the die and the product has been given by the experiment and Lames' formula. The results has been compared with the previous another method. The study has given useful results for the deformation history of the die and the product through the experiment and Lame's formula in backward extrusion which can be applied in the die design for the product with accurate dimension

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.76-79
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• 1999

The study has been performed for the relation between die and product in forward extrusion by the experiment. Strains of the die have been given by the simple experiment using the strain gauge located at the outer surface of the die and the history of the deformation of the die and product is given by the experiment and Lame's formula. The inner pressure of the die causes the deformation of die that affects the accuracy of dimension and shape of product. The product with accurate dimension and shape can be obtained by analysing elastic deformation of the die during process. The deformation of the die during metal forming process has been usually predicted by the experience of industrial engineer or finite element analysis. But it is difficult to predict the dimension of product at unloading and ejected states. The study has given useful results for the deformation history of the die and product through the experiment and Lame's formula at forward extrusion for solid cylinder and can be applied to the die design for product with accurate dimension.

• Transactions of Materials Processing
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• v.8 no.6
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• pp.563-568
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• 1999

The study has been performed for the relation between die and product in closed die upsetting by the experiment. The strain of die has been given by the simple experiment using the strain gauge located at the outer surface of die and the deformation history of die and product has been given by the experiment and Lame's formula. The inner pressure of die causes the deformation of die that affects the accuracy of dimension and shape of product. The product with accurate dimension and shape can be obtained by analysing elastic deformation of die during upsetting process. The deformation of die during metal forming process has been usually predicted by the experience of industrial engineers or finite element analysis. But it is difficult to predict the dimension of product at unloading and ejected states. The study has given useful result for the deformation history of die and product through the experiment and Lame's formula at closed die upsetting, and can be applied in the die design for product with accurate dimension.

• Transactions of Materials Processing
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• v.10 no.1
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• pp.75-79
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• 2001

The study has been performed for the relation between die and product during forward extrusion by the experiment. Stains of the die have been given by the simple experiment using the strain gauge located at the outer surface of the die. The history of the deformation of the die and the product has been given by the experiment and Lame's formula. The inner pressure of the die causes the deformation of die that affects the accuracy of dimension as well as shape of the product. The product with accurate dimension and shape can be obtained by analysing elastic deformation of the die during the process. The deformation of the die during metal forming process has been usually predicted by the experience of industrial engineer or finite element analysis. But it is difficult to predict the dimension of the product at unloading and ejected states. In the present study, useful results for the deformation history of the die and the product were obtained through the experiment and Lame's formula in forward extrusion which can be applied to the die design for the product with accurate dimension.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.305-315
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• 2015

Recently, Jianxin Liu, Hao Pan and Yong Zhang in [On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. 25 (2014), no. 9, 680-685] established an explicit formula for the integral of the product of several Appell polynomials. Their work generalizes all the known results by previous authors on the integral of the product of Bernoulli and Euler polynomials. In this note, by using a special case of their formula for Euler polynomials, we shall provide several reciprocity relations between the special values of Tornheim's multiple series.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.77-84
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• 2000

The product of two localization operators with symbols F and G in some subspace of $L^2(C^n)$ is shown to be a localization operator with symbol in $L^2(C^n)$ and a formula for the symbol of the product in terms of F and G is given.