N four-bar mechanism 2005-08-30 Dynamic simulation of an assembly of 40 four-bar linkages Laboratorio de Ingeniería Mecánica Manuel González Castro Manuel González Castro González Castro Manuel J. Lolo Universidad de la Coruña Laboratorio de Ingeniería Mecánica Escuela Politécnica Superior lolo@cdf.udc.es +34 981337400 Mendizabal s/n Ferrol 15403 España

The one degree-of-freedom assembly of N four-bar linkages is composed by 2N+1 links of 1 m length with a uniformly distributed mass of 1 kg. The system is under gravity effects (9.81 N/kg acting in the negative y direction).

Assembly of N four-bar linkages

This system is a typical example of mechanism that undergoes singular configurations. When the mechanism reaches the horizontal position, the number of degrees of freedom instantaneously increases from 1 to N+1.

The analysis to be performed is a dynamic simulation with a duration of 20 s. Initially, the system (particularized for N=40) is in the position shown in the figure, and the velocity of the x-coordinate of point B0 is 1 m/s.

The reference solution for this problem is the time-history of the position and velocity of point B0 (x and y coordinates). The maximun allowed errors are 1.0E-1 (low precission) and 1.0E-3 (high precission), measured with 400 output steps and a threshold value of 1.0E-3.

The following information is provided:

  1. Time-history of the position and velocity of point B0, as text data file: A02_solution_data.txt
  2. Animation of the system, as AVI movie (first 10 s): A02_solution_movie.avi
  3. Time-history of the position and velocity of point p1, as plot (first 10 s):

    Time-history of the coordinates of point B0

 CPU-time spent by the software to solve the problem (in s).