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Calculating basic linear speed and forces

There are many factors to consider when designing a motion simulator. One is how fast should it move for a good experience. Generally the speed needed is a bit subjective and is significantly affected by design choices, but general wisdom suggests between 150-700mm/s http://www.xsimulator.net/community/threads/minimum-rpm-needed-for-a-2dof.7009/

You can design a motion simulator based on the collective wisdom of the community, without going into detailed calculations. But if your ideas are outside the mainstream it is worth delving into a little mathematics to work out basic speed and force that is available from a particular motor/design combination.

To give some comparable performance context for DC motors and wormdrive gearboxes, here are the specification for the SCN linear actuators, which are often found on commercial simulators:

A SCN6 runs 200mm/sec max. speed, which is a linear velocity of 0.2 m/s: http://miraiintertech.com/home/scn6.php

A SCN 5 runs 400mm/sec max. speed, which is a linear velocity of 0.4 m/s: http://miraiintertech.com/home/scn5.php

For the purpose of the exercise these motors are used as the basis for the example of calculating linear speed and forces, but calculations will be included for different CTC levers and gear ratios: https://www.motiondynamics.com.au/worm-drive-motor-12v-24v-200w-180-rpm-20nm-torque.html

The linear velocity is how fast the motor arm moves for a given Center To Center distance. You can divide the motor torque by the CTC to calculate Newtons. Note the outcome is a trade off between speed and force.

Use this calculator to work out linear speeds from RPMs and CTC lever length: http://www.endmemo.com/physics/rpmlinear.php

A 3600rpm/25:1 with 60mm CTC at 144 rpm gives a linear velocity of 0.9047808 m/s with 333 Newtons.

A 3600rpm/25:1 with 50mm CTC at 144 rpm gives a linear velocity of 0.753984 m/s with 400 Newtons.

A 3600rpm/25:1 with 40mm CTC at 144 rpm gives a linear velocity of 0.6031872 m/s with 500 Newtons.

A 3600rpm/25:1 with 25mm CTC, which is as small as it is practical to go, at 144 rpm gives a linear velocity of 0.376992 m/s with 800 Newtons.

A 3600rpm/50:1 with 40mm CTC at 72 rpm gives a linear velocity of 0.3015936 m/s with 1000 Newtons.

A 3600rpm/60:1 with 40mm CTC at 60 rpm gives a linear velocity of 0.251328 m/s with 1200 Newtons.

You can then take the known Newton for a given CTC, the distance from the motor to the pivot point and the angle used. Run that through the calculator gives you the magnitude of the torque that is possible per motor. Again the angle affects the outcome.

If 500 Newtons is applied 600mm from the pivot at a 90 degree angle then the magnitude of the torque is 300 N m.

If 500 Newtons is applied 600mm from the pivot at a 30 degree angle then the magnitude of the torque is 150 N m.

Disregarding mechanical loss, to know what Newtons it will take to move something it will be Mass (kg) x Acceleration (m/s) = F (N). So to move 100kg at 0.7 m/s needs 70 N. It takes 9.8N per kg to counteract gravity. Keep in mind there is significant mechanical loss in things like the gearbox, depending on the ratio you may want to allow between 10% to 50% loss for worm gears and the greater the gear ratio the higher the % loss is: http://www.meadinfo.org/2008/11/gear-efficiency-spur-helical-bevel-worm.html

If you use pulleys for your simulator ... so you need some torque and speed calculations
RacingMat, speedy, F1Nut and 4 others like this.
Design Considerations & Resources
Apr 7, 2015
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