TY - JOUR
ID - 17099
TI - Development of an Educational Code of Deriving Equations of Motion and Analyzing Dynamic Characteristics of Multibody Closed Chain Systems using GNU Octave for a Beginner
JO - Journal of Applied and Computational Mechanics
JA - JACM
LA - en
SN -
AU - Park, Y.H.
AD - Department of Mechanical Engineering, Yuhan University, 590, Gyeongin-ro, Bucheon-si, Gyeonggi-do, Republic of Korea
Y1 - 2022
PY - 2022
VL - 8
IS - 1
SP - 232
EP - 244
KW - GNU Octave
KW - Multi-body dynamics
KW - Closed chain
KW - Lagrange multiplier
KW - Differential Algebraic Equation
KW - Automation
DO - 10.22055/jacm.2021.38021.3132
N2 - In this study, an automatic GNU Octave code, a free high-level language, for the educational purposes was developed to derive equations of motion and constrain equations of a multibody closed chain system and to calculate the response of the system. The code for calculating the dynamic response was developed by formulating several equations in symbolic expression and extracting differential-algebraic equations in matrix form. The code has a similar structure to the previous code for the open chained system, but it deals with the constraint equation and different numerical integration. The examples of closed chain systems provide an additional procedure to derive the constraint equations by using Lagrangian multiplication theory and to solve the differential-algebraic equations using the Runge-Kutta method. The code was made to understand the theory of analysis and the structure of calculation easily. In addition, the code has an automatic process of the derivation of the Lagrange equation and the constraint equations in matrix form after inputting the number of symbolic information such as position and velocity coordinates and design variables of the system that the user wants to review. The code was validated by comparing the dynamic response of the four-bar linkage with the same design variables and initial conditions of the previous work. By using the code, the reader's ability to exchange information such as symbols and matrices will be expected to be improved.
UR - https://jacm.scu.ac.ir/article_17099.html
L1 - https://jacm.scu.ac.ir/article_17099_dfab730718d9499df8a212038e982383.pdf
ER -