• Journal of the Korean Society for Precision Engineering
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• v.20 no.4
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• pp.103-111
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• 2003

The Denavit-Hartenberg symbolic notation provides the framework for the convenient and systematic method for the robot manipulator kinematics, but is limited its use to the lower pair mechanism or to the single loop mechanisms. The Sheth-Uicker notation is its revised and generalized version to be extended fur the entire domain of the link mechanism including the higher pairs. This paper proposes the method that uses the Sheth-Uicker notation fur the robot kinematics modeling. It uses the instantly coincident coordinate system and the closed loop chain fur the coordinate transformation. It enables us to model the velocity kinematics of the robot that has the complex structures such as the ternary links and the wheels in a systematic and rational way. As an implementation of the proposed method, the Jacobian matrices were obtained for not only the robot with two legs and a torso, but a manipulator on a mobile platform.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.4
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• pp.548-555
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• 2022

This paper describes the hardware implementation of elliptic curve cryptography (ECC) used as a core operation in elliptic curve digital signature algorithm (ECDSA). The ECC processor supports eight operation modes (four point operations, four modular operations) on the NIST P-521 curve. In order to minimize computation complexity required for point scalar multiplication (PSM), the radix-4 Booth encoding scheme and modified Jacobian coordinate system were adopted, which was based on the complexity analysis for five PSM algorithms and four different coordinate systems. Modular multiplication was implemented using a modified 3-Way Toom-Cook multiplication and a modified fast reduction algorithm. The ECC processor was implemented on xczu7ev FPGA device to verify hardware operation. Hardware resources of 101,921 LUTs, 18,357 flip-flops and 101 DSP blocks were used, and it was evaluated that about 370 PSM operations per second were achieved at a maximum operation clock frequency of 45 MHz.

• Journal of Broadcast Engineering
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• v.1 no.2
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• pp.176-187
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• 1996

This paper deals with the accurate estimation of 3- D pose (position and orientation) of a moving object with reference to the world frame (or robot base frame), based on a sequence of stereo images taken by cameras mounted on the end - effector of a robot manipulator. This work is an extension of the previous work[1]. Emphasis is given to the 3-D pose estimation relative to the world (or robot base) frame under the presence of not only the measurement noise in 2 - D images[ 1] but also the camera position errors due to the random noise involved in joint angles of a robot manipulator. To this end, a new set of discrete linear Kalman filter equations is derived, based on the following: 1) the orientation error of the object frame due to measurement noise in 2 - D images is modeled with reference to the camera frame by analyzing the noise propagation through 3- D reconstruction; 2) an extended Jacobian matrix is formulated by combining the result of 1) and the orientation error of the end-effector frame due to joint angle errors through robot differential kinematics; and 3) the rotational motion of an object, which is nonlinear in nature, is linearized based on quaternions. Motion parameters are computed from the estimated quaternions based on the iterated least-squares method. Simulation results show the significant reduction of estimation errors and also demonstrate an accurate convergence of the actual motion parameters to the true values.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.6
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• pp.1083-1091
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• 2017

This paper describes a design of cryptographic processor supporting 224-bit elliptic curves over prime field defined by NIST. Scalar point multiplication that is a core arithmetic function in elliptic curve cryptography(ECC) was implemented by adopting the modified Montgomery ladder algorithm. In order to eliminate division operations that have high computational complexity, projective coordinate was used to implement point addition and point doubling operations, which uses addition, subtraction, multiplication and squaring operations over GF(p). The final result of the scalar point multiplication is converted to affine coordinate and the inverse operation is implemented using Fermat's little theorem. The ECC processor was verified by FPGA implementation using Virtex5 device. The ECC processor synthesized using a 0.18 um CMOS cell library occupies 2.7-Kbit RAM and 27,739 gate equivalents (GEs), and the estimated maximum clock frequency is 71 MHz. One scalar point multiplication takes 1,326,985 clock cycles resulting in the computation time of 18.7 msec at the maximum clock frequency.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.437-442
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• 2012

To analyze a multibody system, this paper proposes an implicit numerical integration method for joint coordinates subsystem synthesis method. To verify the proposed method, a multibody model for an unmanned robot vehicle, which consists of six identical independent suspension systems, is developed. The symbolic method is applied to compute the system Jacobian matrix for the implicit integration method. The proposed method is also verified by performing rough terrain run-over simulation in comparison with the conventional implicit integration method. In addition, to evaluate the efficiency of the proposed method, the CPU time obtained by using this method is compared with that obtained by using the conventional implicit method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1433-1441
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• 2009

In multibody dynamic analysis, one of the most important problems is to reduce computation times for real-time simulation. This paper presents the derivation procedure of equations of motion of a 6${\times}$6 autonomous vehicle in terms of chassis local coordinates which do not require coordinates transformation matrix to enhance efficiency for real-time dynamic analysis. Also, equations of motion are derived using the VT(velocity transformation) technique and symbolic computation method coded by MATLAB. The Jacobian matrix of the equations of motion of a system is derived from symbolic operations to apply the implicit integration method. The analysis results were compared with ADAMS results to verify the accuracy and approve the feasibility of real time analysis.

• 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.

• Journal of the KSME
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• v.31 no.7
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• pp.616-625
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• 1991

운동하는 임의 강체의 순간속도는 플뤼커의 축좌표에 의한 트위스트로 표현될 수 있고 마찬가 지로 직렬형 로봇의 손의 운동 또한 한 개의 트위스트로써 순간속도를 표현할 수 있었으며, Jacobian이 나선좌표로 구성되어 있음을 알았다. 한편, 강체에 작용하는 힘은 플뤼커의 방사좌 표에 의한 치로 표현될 수 있으며, 역관계에 있는 두 나선에 의하여 표현된 트위스트와 치가 로봇의 역학적 해석에 어떻게 이용되는 가를 예를 들어 설명하였다. 이처럼 나선이론은 다 자 유도를 갖는 로봇의 운동 및 역학적 해석에 이용될 수 있는 효과적인 수학적도구라 할 수 있다. 나선은 하나의 기하적 요소이며, 복잡한 강체의 운동을 표현함에 있어서 간편함을 제공한다. 이미 한 세기 전 쯤에 소개된 나선이론이 근래에 와서 이와 같이 로봇의 운동해석에 활용되고 있음은 이러한 때문이라 할 수 있겠다. 나선이론은 이 글에서 설명이 생략된 로봇의 동역학적 해석에도 활용되며, 또한 병렬형 구조를 갖는 로봇(parallel robots)의 해석 등에서도 찾아 볼 수 있다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1640-1648
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• 1991

본 연구에서는 이러한 편사 함수 최소화의 방법을 적용함에 있어 보다 안정된 수렴성과 계산 시간을 단축시키기 위하여 근접 위치 방법(near position method)을 개 발하여 적용하였다. 근접 위치 방법이란 이론적 해석법으로 풀기가 불가능한 기구학 을 갖는 6관절 로봇을 반복적 해석법을 사용한다는 것을 전제로 하여, 초기 위치를 목 표 위치에 가능한 근접하게 잡아서 반복 계산을 수행하는 방법으로써 로봇의 기구학적 자세에 따른 수렴의 불안정성을 방지하고, 계산 시간을 단축하는데 그 목적이 있다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.899-909
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• 1992

An iterative solution technique is presented to analyze the dynamic systems of rigid bodies subjected to kinematic constraints. Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Constraints on the velocity and acceleration as well as the position are made to be satisfied at joints at each time step. Time integration is efficiently performed because decomposition or orthonormalization of the large matrix is not required at all. An acceleration technique is suggested for the faster convergence of the iterative scheme.