From ee70bbbb6f2c323d27d6698a01cfb982e58296a6 Mon Sep 17 00:00:00 2001
From: Ahmed Alaali <aqahmed17@gmail.com>
Date: Fri, 30 May 2025 22:37:47 +0300
Subject: [PATCH] Huh

---
 README.md | 144 +++++++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 138 insertions(+), 6 deletions(-)

diff --git a/README.md b/README.md
index 931c239..a7d9d02 100644
--- a/README.md
+++ b/README.md
@@ -49,7 +49,7 @@ The design is a compact, scalable cycloidal gearbox featuring two cycloidal disc
 
 #### 4. List of Materials & Components
 
-##### Standard Components
+- ##### Standard Components
 
 | Part          | Quantity | Approx. Size                                       | Notes                   |
 | ------------- | -------- | -------------------------------------------------- | ----------------------- |
@@ -57,7 +57,7 @@ The design is a compact, scalable cycloidal gearbox featuring two cycloidal disc
 | Bearing       | 4        | Ø32 mm (outer) × Ø20 mm (inner) × 7 mm (thickness) | Disc and input supports |
 | Stepper Motor | 1        | NEMA-17                                            | Input source            |
 
-##### Bolts & Nuts (*with available size approximations*)
+- ##### Bolts & Nuts (*with available size approximations*)
 
 Note: If a bolt is slightly longer than needed, it can be trimmed using a saw. Nut sizes should fit snugly but not too tight.
 
@@ -81,7 +81,139 @@ Note: If a bolt is slightly longer than needed, it can be trimmed using a saw. N
         - May require slight sanding to fit perfectly.
     - 1 × Nut: M3 (Edge-to-edge ≈ 5.4 mm, Thickness ≈ 2.5 mm)
 
-##### 3D-Printed Components
-- Material: PLA (tested), PETG (recommended for durability)
-- Parts: Housing, base cover, discs, shaft connectors, output caps, circlips
-- Infill: Suggested 40% or more for torque applications
+- ##### 3D-Printed Components
+    - Material: PLA (tested), PETG (recommended for durability)
+    - Parts: Housing, base cover, discs, shaft connectors, output caps, circlips
+    - Infill: Suggested 40% or more for torque applications
+
+#### 5. Cycloidal Drive Strength Analysis
+
+---
+
+##### **1. Motor Output Torque**
+
+* **Motor Stall Torque**: 0.45 Nm
+* **Gear Ratio**: 21:1
+* **Estimated Efficiency**: 85%
+
+$$
+\text{Output Torque} = 0.45 \times 21 \times 0.85 = \boxed{8.03 \, \text{Nm}}
+$$
+
+---
+
+##### **2. Load Handling Capability (Based on PLA Disc)**
+
+###### PLA Parameters:
+
+* **Yield Strength of PLA**: 50 MPa
+* **Safety Factor**: 3 → Allowable stress = 16.7 MPa
+* **Contact Area (per lobe)**: 5 mm²
+* **Lobes in contact**: 4
+* **Radius from center to lobe force point**: 33.5 mm = 0.0335 m
+* **Infill Density**: 25%
+
+###### Calculations:
+
+* **Force per lobe**:
+
+$$
+F_{\text{lobe}} = 16.7 \times 10^6 \times 5 \times 10^{-6} = 83.5 \, \text{N}
+$$
+
+* **Total force from 4 lobes**:
+
+$$
+F_{\text{total}} = 4 \times 83.5 = 334 \, \text{N}
+$$
+
+* **Torque handling at 33.5 mm radius**:
+
+$$
+\tau = 334 \times 0.0335 = 11.2 \, \text{Nm}
+$$
+
+* **Account for 25% infill**:
+
+$$
+\tau_{\text{safe}} = 11.2 \times 0.25 = \boxed{2.8 \, \text{Nm}}
+$$
+
+---
+
+##### **3. Drive Pin Strength (Bolts with PLA Sleeves)**
+
+###### Assumption:
+
+* Bolts used instead of precision 5 mm mild steel pins
+* Outer diameter maintained at **5 mm** using **PLA sleeves**
+* Inner bolt shaft assumed 4 mm (typical M4 bolt shank)
+* **Steel Yield Strength: 260 MPa**
+
+###### Cross-sectional Area (4 mm bolt):
+
+$$
+A = \frac{\pi D^2}{4} = \frac{\pi \cdot 4^2}{4} = 12.57 \, \text{mm}^2
+$$
+
+* **Force per bolt**:
+
+$$
+F_{\text{bolt}} = 260 \times 12.57 = 3,268.2 \, \text{N}
+$$
+
+* **Total force (4 bolts)**:
+
+$$
+F_{\text{total}} = 4 \times 3,268.2 = 13,072.8 \, \text{N}
+$$
+
+* **Torque capacity**:
+
+$$
+\tau = 13,072.8 \times 0.0335 = \boxed{437.9 \, \text{Nm}} \quad \text{(Safe✅)}
+$$
+
+> Note: **PLA sleeves** do not contribute significantly to strength — they act as spacers or guides. Only **steel bolts** are load-bearing.
+
+---
+
+##### **4. Max Load at 50 mm Arm**
+
+$$
+F = \frac{\tau_{\text{safe}}}{r} = \frac{2.8}{0.05} = 56 \, \text{N}
+$$
+
+$$
+\text{Mass} = \frac{56}{9.81} = \boxed{5.7 \, \text{kg}}
+$$
+
+---
+
+##### Final Summary Table
+
+| Category                    | Value    | Safe?                    |
+| --------------------------- | -------- | ------------------------ |
+| Motor Stall Torque          | 0.45 Nm  | ✅                        |
+| Output Torque               | 8.03 Nm  | ❌ Exceeds PLA safe limit |
+| PLA Torque Limit            | 2.8 Nm   | ✅                        |
+| Bolt + PLA Pin Torque Limit | 437.9 Nm | ✅ (way overbuilt)        |
+| Max Load (at 50 mm arm)     | 5.7 kg   | ✅                        |
+
+---
+
+##### Final Conclusion
+
+The **cycloidal drive system is likely to fail at the PLA disc lobes under full output torque**, especially if printed with only **25% infill**. Although the **bolts (with PLA sleeves)** acting as drive pins are structurally sufficient, the **PLA disc is the mechanical weak point**.
+
+##### If tested:
+
+* The drive **will function under light loads (below \~5.7 kg at 50 mm arm)**.
+* Under full load or high-torque demand, **plastic deformation or cracking is expected at the lobes**.
+* The bolts will hold without issue, but **localized PLA wear or failure around the lobes and sleeves is likely.**
+
+##### Recommendations:
+
+* Increase **infill to at least 75%** or use a stronger material like **PETG**.
+* Consider **fillet reinforcement** around lobes to distribute stress.
+* Reduce gear ratio or torque output if high load isn't needed.
\ No newline at end of file