Time-aware kinematics

Kimech separates the coordinate used to parameterize configurations from the optional physical time associated with requested samples.

For one Driver coordinate (u), a geometric sweep represents

[ q = q(u). ]

If the prescribed coordinate is known as a function of physical time,

[ u = u(t), ]

then the same samples may also represent

[ q = q(t). ]

Constant-speed example

import numpy as np

time = np.linspace(0.0, 2.0, 201)
theta0 = np.deg2rad(30.0)
omega = 5.0

driver = KinematicDriver(
    crank_joint,
    position=theta0 + omega * time,
    velocity=omega,
    acceleration=0.0,
)

solution = solve(
    mechanism,
    driver=driver,
    time=time,
    initial_guess=initial_guess,
)

The Driver contains the prescribed coordinate and its physical derivatives. time belongs to the solve history.

What time does

When supplied, time:

• contains one physical instant per requested Driver sample;

• is retained as solution.time;

• is propagated to solution[i].time;

• must be finite and strictly increasing for a multi-sample solve.

What time does not do

Supplying time does not:

• change the continuation parameter from (u) to (t);

• numerically integrate the mechanism;

• numerically differentiate Driver positions;

• infer missing Driver velocity or acceleration;

• verify that user-supplied position, velocity, and acceleration histories are mutually consistent.

A timed and untimed solve evaluated at the same Driver samples therefore have the same kinematic state. Time adds physical sample association only.