## Calculations

**Rotational Stage** Direct Drive

Using the above equation will provide the necessary torque required for the stepper motor to have.

**Definitions:**

p = Density of Chuck (oz/in3) = 4.48

L = Length of Chuck (in) = 3 1/16

r^{2} = Radius of Chuck (in) = 3/4

N = Angular Velocity of Load (RPM) = max 400

t_{a} = Time to Accelerate (seconds) = 0.075

**Linear Stage** Lead Screw

Using the addition of these two Equations will provide the necessary torque required for the stepper motor to have.

**Definitions:**

d^{2} = Lead of Screw (in/rev) = 0.025

W_{L&C} = Weight of load and carriage (oz)
≈ 40 oz

e = mechanism efficiency = 75-85%

p = Density of Lead Screw (oz/in3) = 0.289 (lb-in) = 4.64 (oz-in)

L = Length of Lead Screw (in) = 12

r_{2} = Radius of Lead Screw (in) = 3/16

V_{Load} = Linear Velocity of Load (in/sec) =
1.25

t_{a} = Time to Accelerate (seconds) = 0.075

u =Coefficient of Friction = 0.001

## Motor Choice

From McMaster-Carr: NEMA 11 Frame MotorsTorque (lb-in): 0.860

Full Load Amps: 0.67

Part Number: 6627T22

Each: $99.74

**Rationale:**

- Motor Torque lb-in is slightly greater than calculated value to account for any possible underestimation in calculations
- Using the same motor for both applications to account for easy replacement

**Document Links**

System Drawings | Stages | Chuck | Motion Controller | Digital Micrometer | Additional Hardware | Measurement Logic | Bill of Materials