• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.1
• /
• pp.102-109
• /
• 1986

Based on the Hartenberg-Denavit symbolic equation, which is one of equations for the kinematic analysis of three dimensional (3-D) linkage, a generalized kinematic motion equation is derived utilizing Euler angles and employing the coordinates transformation. The derived equation can feasibly be used for the motion analysis of any type of 3-D linkages as well as 2-D ones. In order to simulate the general motion of 3-D linkgages on digital computer, the generalized equation is programmed through the process of numerical analysis after converting the equation to the type of Newton-Raphson formula and denoting it in matrix form. The feasibility of theoretically derived equation is experimentally proved by comparing the results from the computer with those from experimental setup of three differrent but generally empolyed 3-D linkages.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.4
• /
• pp.577-584
• /
• 1986

본 연구에서는 측정자가 시간과 노력을 소비하면서 3차원 연쇄기구의 공간운 동을 유추적으로 측정한 현재까지의 실험측정을 지양하고, 국내에서 구입 가능하고 염 가인 Apple II와 같은 같은 마이크로 컴퓨터 또는 마이크로프로세서를 이용, 3차원 연 쇄기구의 공간운동을 신속하고 정확하게 측정분석하는 자동 실험장치를 설계 제작한 다음, 이 장치를 일반 3차원 연쇄기구 모델에 적용 측정된 결과를 기호방정식을 이용 한 일반 연쇄기구 운동식의 이론 결과와 비교 검토하였다.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.1
• /
• pp.35-43
• /
• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.6
• /
• pp.1509-1517
• /
• 1993

The purpose of this study is to develop a program for the automatic derivation of the symbolic equations necessary for the kinematic and dynamic analyses of the spatial mechanism. For this purpose, a symbolic manipulation package called MCSYMA is used. Every symbolic equation is formulated using relative joint coordinate to obtain the numerically efficient system equations. These equations are produced in FORTRAN statements and linked to a FORTRAN program for numerical analysis. Several examples are taken for comparison with the commercial package called DADS which is using Cartesian coordinate approach. Also, this symbolic formulation approach is compared with a conventional numerical approach for an example. The results show that this symbolic approach with relative joint coordinate system is most efficient in computational time among three and is recommended for the derivation of macro elements frequently used.