I'm trying to make a dynamic model of pick-and-place manipulator called T-gantry.
This robot consists of two servo drives connected with tooth belt and end effector, on a cross base.
I've already assembled a dynamic model of an simplified model:
That is described by a motion equation:
(T1/r1) + (T2/r2) + F_ext = x'' * ( (J1/r1^2) + m + (J2/r2^2) ), where
T1, T2 - torques of servos
F_ext - external force
x'' - acceleration of the mass
J1, J2 - moments of inertia of servos
m - mass
r1, r2 - radii of the pulleys.
Now I want to assemble a two equation model describing movement of end effector, where
OUTPUT = acceleration in axis x and y, i.e. : x'' and y''
INPUT = torques T1 and T2