linkage_simulation

Simulates the kinematics of various linkage mechanisms for traversing monkey-bars

usage

run klann_simulation.py or pantograph_simulation.py to generate interactive simulation plots

requirements

pip install -r requirements.txt

• simulation utilizes numpy, scipy, and matplotlib
• reading data from motiongen files requires tabula-py (which depends on pandas)

choosing simulations

scroll to the bottom of either simulation file. Under if __name__ == '__main__', comment/uncomment the function calls to choose the desired output

modifying geometry

the functions kinematics_sim(), two_phase(), and three_phase() each start with a dictionary which defines the geometric constants of the linkage system, for example:

kwargs = dict(
    cycles = 4,                                   # number of cycles, each cycle being 2*pi rotation of L1
    grab = 2/3*np.pi,                             # point along cycle where link attached to bar
    release = 4/3*np.pi,                          # point along cycle where link releases from bar
    L = [2.078, 1.016, 1.906, 1.196, 1.886, 1.789, 3.15, 2.251, 5.686],  # lengths 0-8
    phi = np.deg2rad(32.5),                       # fixed acute angle between L2 & L5
    input_angle = np.deg2rad(210),                # starting angle of input link, L1
    input_angular_velocity = 1,                   # constant input ang. vel. for velocity sim
    theta0 = np.pi,                               # fixed angle between ground points
    theta_constraint = np.deg2rad(-58),           # meaning varies for different linkage systems
    paths = [8, -1]                               # indices of the joints of which to trace the movement path (origin is the last column)
)

meaning of theta_constraint and phi

• for the klann mechanism:
  • theta_constraint = theta4, as shown in reference/variable_diagram.pdf
  • phi is the fixed acute angle between L2 and L5, as shown in reference/variable_diagram.pdf
• for the pantograph:
  • theta_constraint is the difference in angle between L1 and L2, where L1 is driven and L2 is geared to L1
  • phi is the angle between L4 and L5, which is the angle of the corner of the ternary link that is connected to the driven link (L1)

units

reference/dimensions.pdf and motiongen/klann_mechanism use millimeters, the default values in the python files are in inches (will be converted)

motiongen.io integration

In the motiongen folder, there's a .motiongen file that can be opened by going to motiongen.io and importing the file. If you make changes and export to a pdf, then replace that pdf with the one currently in the motiongen folder, the simulation scripts will read in the new geometry. (Do not add/remove links in motiongen, if any of the link numbers change, the simulation scripts will break)

output