# Motion Control Cheat Sheet & Unit Conversions

## UNITS & FORMULAE

#### COMMON ENGINEERING UNIT CONVERSIONS – BASIC UNITS

Parameter (Basic Units) mass (m) SI Units English/American Units kilogram (kg) pound mass (lbm) meter (m) foot or inch (ft or in) second (s) Ampere (A)

#### DERIVED UNITS

Parameter (Derived Units) Force – weight (F or W) SI Units English/American Units Newton (N) pound or ounce (lbf or oz) Newton-meter (Nm) foot-pound (ft-lb or in-lb) Joule (J) foot-pound (ft-lb or in-lb) Watt (W) horsepower (hp or W) Volt (V) ohms (Ω) kilogram-meter2 (kg-m2) inch-pound-second2 (in-lb-s2) radian (rad) degree or radian (deg or rad) revolution (rev) meter per sec. (m/s) inch per second (in/s) meter per second2 (m/s2) inch per second2 (in/s2) rad per second (rad/s) rev per minute (rpm) rad per second2 (rad/s2)

#### BASIC DEFINITIONS & FORMULAE

Parameter Formula Force – accel (F = m * a) SI Units Formula English/American Units Formula 1 N = 1 kg * 1 m / s2 1 lbf = 1 lbf / (386 in / s2) * 386 in / s2 1 Nm = 1 kg-m2 * 1 rad / s2 1 in-lb = 1 in-bl-s2 * 1 rad / s2 1 V = 1 A * 1 Ω 1 J = 1 N * 1 m 1 in-lb = .113 Nm = .113 Ws = .113 J 1 J = 1 V * 1 A * 1 s 1 W = 1 N * 1 m / s 1 hp = 550 ft-lb / s = 745.7 W 1 W = 1 Nm * 1 rad / s (note: radians have no units) 1 W = 1 V * 1 A 1 W = 1 J / 1 s 1 W = 1 A2 * 1 Ω

#### MOTOR CONSTANTS

Parameter Formula Torque const (Kt = T / I) SI Units Formula English/American Units Formula Kt = Nm / A Kt = in-lb / A Ke = V / (rad / s) Ke = V / krpm

#### SERVO MOTOR FORMULAE

Parameter Formula Current Draw (I + T / Kt) SI Units Formula English/American Units Formula 1 A = 1 Nm / (Nm / A) 1 A = 1 in-lb / (in-lb / A) 1 V = AΩ + V / (rad / s) * (rad / s) 1 V = AΩ + V / (krpm) * (krpm)

### CONVERSIONS

To convert from units of A to units of B, find the value at the intersection of A and B, then multiply your number by this value. Example: to convert from cm to microns, multiply value in cm by 1.00E+04.

#### LENGTH CONVERSION

A (below) B (right) micron (µm) mm cm m in micron (µm) mm cm m in ft 1 0.001 1.00E-04 1.00E-06 3.94E-05 3.28E-06 1000 1 0.1 0.001 0.03937 3.28E-03 1.00E+04 10 1 0.01 0.3937 0.03281 1.00E+06 1000 100 1 39.37 3.281 2.54E+04 25.4 2.54 0.0254 1 0.0833 3.05E+05 302.8 30.48 0.3048 12 1

#### MASS CONVERSION

A (below) B (right) g kg slug ozm g kg slug ozm lbm 1 0.001 6.85E-05 0.0353 2.20E-03 1000 1 6.85E-02 35.274 2.2046 1.46E+04 14.59 1 514.78 32.17 28.35 0.0284 1.94E-03 1 0.0625 453.6 0.4536 0.0311 16 1

#### FORCE CONVERSION

A (below) B (right) N kgf gf ozf N kgf gf ozf lbf 1 0.102 101.97 3.596 0.225 9.81 1 1000 35.274 2.205 9.81E-03 0.001 1 0.0353 2.21E-03 0.28 0.0283 28.351 1 0.0625 4.45 0.4536 453.6 16 1

#### TORQUE CONVERSION

A (below) B (right) g-cm kg-cm kg-m N-m oz-in lb-in g-cm kg-cm kg-m N-m oz-in lb-in lb-ft 1 0.001 1.00E-05 9.81E-05 0.014 8.68E-04 7.23E-05 1000 1 0.01 0.098 13.89 0.868 0.072 1.00E+05 100 1 9.81 1389 86.8 7.23 1.02E+04 10.2 0.102 1 141.6 8.85 0.738 72.01 0.072 7.21E-04 7.06E-03 1 0.063 5.21E-03 1.15E+03 1.152 0.012 0.113 16 1 0.083 1.38E+04 13.83 0.138 1.356 192 12 1

#### POWER CONVERSION

A (below) B (right) Watts KW Horsepower in-lb/s Watts KW Horesepower in-lb/s ft-lb/s 1 100E-03 1.34E-03 8.85 0.74 1000 1 1.34 8851 738 746 0.746 1 6600 550 0.113 1.13E-04 1.52E-04 1 0.083 1.35 1.36E-03 1.82E-03 12 1

#### LINEAR VELOCITY CONVERSION

A (below) B (right) mm/s cm/s m/s in/s ft/s in/min mm/s cm/s m/s in/s ft/s in/min ft/min 1 0.1 0.001 0.0394 3.28E-03 2.362 0.1968 10 1 0.01 0.394 0.0328 23.62 1.97 1000 100 1 39.37 3.281 2362.2 196.9 25.4 2.54 0.0254 1 0.083 60 5 304.8 30.48 0.3048 12 1 720 60 0.423 0.0423 4.23E-04 0.0167 1.39E-03 1 0.0833 5.08 0.508 5.08E-03 0.2 0.0167 12 1

#### ANGULAR VELOCITY CONVERSION

A (below) B (right) deg/s rad/s rpm deg/s rad/s rpm rps 1 0.0175 0.167 2.78E-03 57.3 1 9.55 0.159 6 0.105 1 0.0167 360 6.28 60 1

#### ROTARY INERTIA CONVERSION

A (below) B (right) g-cm2 kg-cm2 g-cm-s2 kg-cm-s2 kg-m2 lb-in-s2 lb-ft-s2 lb-in2 lb-ft2 oz-in2 g-cm2 kg-cm2 g-cm-s2 kg-cm-s2 kg-m2 lb-in-s2 lb-ft-s2 lb-in2 lb-ft2 oz-in2 oz-in-s2 1 0.001 0.001 1.02E-06 1.00E-07 8.85E-07 7.38E-08 3.42E-04 2.37E-06 5.50E-03 1.42E-05 1000 1 1.02 0.001 0.0001 8.85E-04 7.38E-05 0.342 2.40E-03 5.47 0.014 981 0.981 1 0.001 9.81E-05 8.68E-04 7.23E-05 0.335 2.30E-03 5.36 0.014 9.81E+05 981 1000 1 0.0981 0.868 0.072 335.1 2.33 5362 13.89 1.00E+07 10000 10190 10.19 1 8.85 0.738 3417.74 23.734 54675 141.6 1.13E+06 1130 1.15E+03 1.152 0.113 1 0.083 386.1 2.68 6177 16 1.36E+07 1.36E+04 1.38E+04 13.83 1.36 12 1 4633 32.2 7.41E+04 192 2926 2.93 2.98 0.003 2.93E-04 2.60E-03 2.16E-04 1 6.90E-03 16 0.041 4.21E+05 421.4 429.7 0.43 0.0421 0.373 0.031 144 1 2304 5.97 182.9 0.183 0.187 1.87E-04 1.83E-05 1.62E-04 1.35E-05 0,0625 4.34E-04 1 2.60E-03 7.06E+04 70.62 72 0.072 0.007 0.063 5.20E-03 24.13 0.168 386.1 1  