• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.12
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• pp.723-731
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• 2005

The $4{\times}4$ homogeneous transformation matrix is a compact representation of orientation and position of an object in robotics and computer graphics. A coordinate transformation is accomplished through the successive multiplications of homogeneous matrices, each of which represents the orientation and position of each corresponding link. Thus, for real time control applications in robotics or animation in computer graphics, the fast multiplication of homogeneous matrices is quite demanding. In this paper, a parallel-architecture vector processor is designed for this purpose. The processor has several key features. For the accuracy of computation for real application, the operands of the processors are floating point numbers based on the IEEE Standard 754. For the parallelism and reduction of hardware redundancy, the processor takes column vectors of homogeneous matrices as multiplication unit. To further improve the throughput, the processor structure and its control is based on a pipe-lined structure. Since the designed processor can be used as a special purpose coprocessor in robotics and computer graphics, additionally to special matrix/matrix or matrix/vector multiplication, several other useful instructions for various transformation algorithms are included for wide application of the new design. The suggested instruction set will serve as standard in future processor design for Robotics and Computer Graphics. The design is verified using FPGA implementation. Also a comparative performance improvement of the proposed design is studied compared to a uni-processor approach for possibilities of its real time application.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.681-689
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• 2019

The $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is an orbit of a subgroup of the $M{\ddot{o}}bius$ transformation group of ${\mathbb{S}}^{n+1}$. In this note, We prove that a compact $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is the image of a $M{\ddot{o}}bius$ transformation of the isometric homogeneous submanifold in ${\mathbb{S}}^{n+1}$.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.265-265
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• 2000

In this paper the systematic modeling method of general wheeled mobile robot is proposed. First we show how to describe kinematics properties of wheeled mobile robot in the method formulating constraint equations using Basic Homogeneous Transform(BHT) which is used mainly the kinematics modeling of manipulator, and, under assumption it's provided part of nullvector in given constraint equations, find kinematics model of mobile robot related to actuators in real robot.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.5
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• pp.1-6
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• 2005

In this paper, the natural frequencies of non-homogeneous damped beam are determined by using the differential transformation. The beam considered has different stiffness, damping and mass properties in each of two parts. The various boundary conditions are assumed at each end. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving a non-homogeneous damped beam problem.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.5
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• pp.118-125
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• 2002

The previous kinematic analysis of wheeled mobile robots(WMRs) is performed in an ad-hoc manner, while those of the robot manipulators are done in a consistent way using the coordinate system assignment and the homogeneous transformation matrix. This paper shows why the method for the robot manipulators cannot be used directly to the WMRs and proposes the method for the WMRs, which contains modeling the wheel with the Sheth-Uicker notation and the homogeneous transformation. The proposed method enable us to model the velocity kinematics of the WMRs in a consistent way. As an implementation of the proposed method, the Jacobian matrices were obtained for conventional steered wheel and non-steered wheel respectively and the forward and inverse velocity kinematic solutions were calculated fur a tricycle typed WMR. We hope that our proposed method comes to hold an equivalent roles for WMRs, as that of the manipulators does for the robot manipulators.

• Bulletin of the Korean Chemical Society
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• v.19 no.4
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• pp.408-411
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• 1998

• Journal of the Korean Ceramic Society
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• v.42 no.11 s.282
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• pp.718-721
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• 2005

The high temperature tetragonal phase of zirconia containing $1.40{\~}1.60\;mol\%$ of yttria can be fully retained at room temperature by rapid cooling. The metastable tetragonal phase transforms into the monoclinic phase athermally upon subzero cooling. The transformation exhibited an athermal burst transformation. The effects of yttria content and grain size on the athermal martensitic transformation were studied in detail. The burst temperature linearly decreased with increasing yttria content or decreasing grain size. To consider the distribution of martensite nuclei, the Weibull modulus of the athermal martensitic transformation was evaluated from the distribution of the burst transformation temperature. From the Weibull analysis, the distribution of embryos appears to be more homogeneous than that of the defects responsible for the fracture of similar material.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.102-111
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• 2000

Methodology of volumetric error identification and compensation is presented to improve the accuracy of NC machine tools by using a reference artifact and a touch trigger probe. Homogeneous transformation matrix and kinematic chain are used for modeling the geo-metric and thermal errors of a three-axis vertical machining center. The reference artifact is designed and fabricated to identify the model parameters by machine tool metrology. Parameters in the error model are able to be identified and updated by direct measurement of the reference artifact on the machine tool under the actual conditions which include the thermal interactions of error sources. A volumetric error compensation system based on IBM/PC is linked with a FANUC CNC controller to compensate for the identified volumetric error in machining workspace.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.1017-1021
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• 1995

Geometric and thermal errors are responsible for major components of the errors of a computer numerically controlled turning center. The planar error of a CNC turning center are comprised of 11 geometric and thermal error components. The error synthesis model is formulated by homogeneous coordinate transformation method and expresses the effect of such error components on the planar error of a CNC turning center. In this paper, the sensitivity analysis of the model on the noises through sensing and the change of temperature is addressed. The sensitivity analysis show that the error systhesis model is robust on the noses and z planar error is much affected by the change of temperatures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2899-2908
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• 2000

Methodology of volumetric error identification is presented to improve the accuracy of NC machine tools by using a reference artifact and a touch trigger probe. Homogeneous transformation matrix and kinematic chain are used for modeling the geometric and thermal errors of a three-axis vertical machining center. The reference artifact is designed and fabricated to identify the model parameters by machine tool metrology. Parameters in the error model are able to be identified and updated by direct measurement of the reference artifact on the machine tool under the actual conditions which include the thermal interactions of error sources. The proposed method can speed up and simplify volumetric error identification processes.