02. Concept design
1. Concept design
The formulas on this page are partially assisted by ChatGPT.
Prompt: Calculate the motion accuracy of a robot using a stepper motor nema 17. It works with wheels and an arm, and the calculation is based on a wheel diameter of 50mm and an arm length of 170mm.
A. Approx. dimensions
First, I started designing from the size of general 1 kg spool holder.
B. Required precision
I calculated the XY-axis wheel and Z-axis arm accuracy based on rough dimensions, a 1.8° stepper motor, 170mm arm length, and 50mm wheel diameter. Accuracy can be improved later by adjusting the gear ratio or using "microstepping".
a. Wheel Precision
| Item | Value | Formula |
|---|---|---|
| Wheel Diameter (D) | 50 mm | Input parameter |
| Step Angle (θ) | 1.8° | — |
| Wheel Circumference (C) | 157.08 mm | C = π * D |
| Wheel Movement (d_w) | 0.785 mm/step | d_w = (θ / 360) * C |
b. Arm Precision and Gear Ratio
| Item | Value | Formula |
|---|---|---|
| Arm Length (L) | 170 mm | Input parameter |
| Step Angle (θ) | 1.8° | — |
| Arm Tip Movement (d) | 5.34 mm/step | d = L * sin θ |
| Required Precision (P) | 0.5 mm/step | Input parameter |
| Required Gear Ratio (R) | Approx. 10.7:1 | R = d / P = 5.34 / 0.5 |
C. Estimated weight
I made a very rough weight estimate and it ended up being about the same weight as small 3D printers (such as Kingroon KP3S or BumbLab A1 Mini).
| Name | Weight (kg) | Quantity | Total Weight (kg) |
|---|---|---|---|
| Stepper Motor | 0.3 | 6 | 1.8 |
| Filament Spool | 1 | 1 | 1 |
| Extruder | 0.25 | 1 | 0.25 |
| Battery / power supply | 0.5 | 1 | 0.5 |
| Frame | 0.5 | 1 | 0.5 |
| Others | 0.25 | 1 | 0.25 |
| Total | 4.8 kg |
D. Required torque
b. Arm Torque Calculation
| Item | Value | Formula |
|---|---|---|
| Arm Weight (m) | 0.6 kg | Input parameter |
| Arm Length (L) | 0.17 m | Input parameter |
| Gravity (g) | 9.81 m/s² | — |
| Center of Mass | 0.17 m | Input parameter |
| Load Torque (T_load) | 1.001 N·m | T_load = m × g × L |
| Gear Ratio | 30:1 | — |
| Motor Torque (T_motor) | 3.335 N·cm | T_motor = T_load / Gear Ratio × 100 |
E. Motor selection
F. Omni wheel
I downloaded omni wheel STEP model from McMaster-Carr.