Vernier Scale & Screw Gauge

Cheatsheet Content

### Vernier Scale Basics - **Purpose:** To measure lengths with greater precision than a standard ruler. - **Principle:** Difference between two scales (main scale and vernier scale). - **Least Count (LC):** Smallest measurement that can be made accurately. $$LC = 1 MSD - 1 VSD$$ where MSD = Main Scale Division, VSD = Vernier Scale Division. Alternatively, $$LC = \frac{\text{Value of one MSD}}{\text{Total number of divisions on Vernier scale}}$$ ### Reading a Vernier Scale 1. **Main Scale Reading (MSR):** Note the reading on the main scale just *before* the zero mark of the vernier scale. 2. **Vernier Scale Coincidence (VSC):** Find the vernier scale division that perfectly coincides with *any* main scale division. 3. **Total Reading:** $$\text{Total Reading} = MSR + (VSC \times LC)$$ ### Zero Error (Vernier Scale) - **Positive Zero Error:** When the zero mark of the vernier scale is to the right of the main scale zero mark. $$\text{Positive Zero Error} = + (VSC_{zero} \times LC)$$ where $VSC_{zero}$ is the vernier division coinciding with main scale when jaws are closed. - **Negative Zero Error:** When the zero mark of the vernier scale is to the left of the main scale zero mark. Here, count from the *right* end of the vernier scale. $$\text{Negative Zero Error} = - ((N - VSC_{zero}) \times LC)$$ where N is the total number of divisions on the vernier scale. - **Corrected Reading:** $$\text{Corrected Reading} = \text{Total Reading} - \text{Zero Error}$$ ### Screw Gauge Basics - **Purpose:** To measure very small lengths (e.g., diameter of a thin wire, thickness of a sheet) with high precision. - **Principle:** Conversion of rotational motion into linear motion. - **Pitch:** The distance moved by the screw along the main scale in one complete rotation of the circular scale. $$\text{Pitch} = \frac{\text{Distance moved on main scale}}{\text{Number of full rotations}}$$ - **Least Count (LC):** $$LC = \frac{\text{Pitch}}{\text{Total number of divisions on circular scale}}$$ ### Reading a Screw Gauge 1. **Main Scale Reading (MSR) / Linear Scale Reading (LSR):** Note the reading on the main scale that is visible on the edge of the circular scale. 2. **Circular Scale Coincidence (CSC):** Find the circular scale division that coincides with the main line (datum line) of the main scale. 3. **Total Reading:** $$\text{Total Reading} = MSR + (CSC \times LC)$$ ### Zero Error (Screw Gauge) - **Positive Zero Error:** When the zero mark of the circular scale is *below* the main line (datum line) when the jaws are closed. $$\text{Positive Zero Error} = + (CSC_{zero} \times LC)$$ where $CSC_{zero}$ is the circular scale division coinciding with the datum line when jaws are closed. - **Negative Zero Error:** When the zero mark of the circular scale is *above* the main line (datum line) when the jaws are closed. $$\text{Negative Zero Error} = - ((N - CSC_{zero}) \times LC)$$ where N is the total number of divisions on the circular scale. - **Corrected Reading:** $$\text{Corrected Reading} = \text{Total Reading} - \text{Zero Error}$$