How this calculator works
Thrust must overcome the uphill component of weight, friction on the supporting surface and inertia. Constant-speed mode includes no acceleration term. A symmetric triangular speed profile spends half the move accelerating and half decelerating; a one-way constant-acceleration profile starts from rest and ends at peak speed. Use the friction coefficient appropriate to the limiting phase: static breakaway and running friction can differ. The actuator is assumed parallel to travel, with no linkage or screw efficiency included.
Formula
F = m[a + g sin(theta) + mu g cos(theta)]. Constant speed: v=s/t, a=0. Triangular: a=4s/t², v_peak=2s/t. Acceleration from rest: a=2s/t².
Worked example
A 10 kg load moving horizontally at constant speed with friction coefficient 0.2 and g=10 m/s² needs 20 N. Moving 1 m in 2 s with a triangular profile on a frictionless 30 degree incline needs 60 N peak driving thrust.
Frequently asked questions
Does stroke divided by time give peak speed?
Only at constant speed. The two accelerating profiles here reach twice the average travel speed.
Can I model an actuator pushing at an angle?
Not directly. Resolve the actuator force along the travel direction and account for any added normal force.
What mass should I include?
Include every translating mass driven by the actuator, including fixtures and moving carriage parts.