Mechanical Gear
A mechanical gear is a rotating machine element with teeth that mesh with another toothed component to transmit torque and rotational motion, simultaneously changing speed and mechanical advantage. Gears are fundamental power transmission devices used to increase or decrease rotational speed, multiply torque, or change the direction of motion. They are ubiquitous in automobiles, industrial machinery, watches, and robotics.
Key Formula
N1/N2 = T2/T1 = omega1/omega2
LaTeX: \frac{N_1}{N_2} = \frac{T_2}{T_1} = \frac{\omega_1}{\omega_2}
| Symbol | Meaning | Unit |
|---|---|---|
| N_1 | Number of teeth on driver gear | dimensionless |
| N_2 | Number of teeth on driven gear | dimensionless |
| T_1 | Torque on driver gear | N·m |
| T_2 | Torque on driven gear | N·m |
| \omega_1 | Angular velocity of driver gear | rad/s |
| \omega_2 | Angular velocity of driven gear | rad/s |
Worked Example
Problem
A driver gear with 20 teeth rotates at 1000 rpm and delivers a torque of 50 N·m. It meshes with a driven gear having 80 teeth. Find the speed and torque of the driven gear (assuming 100% efficiency).
Solution
Step 1: Find gear ratio. Gear ratio = N1/N2 = 20/80 = 1/4 Step 2: Calculate speed of driven gear. ω2 = ω1 × (N1/N2) = 1000 × (20/80) = 250 rpm Step 3: Calculate torque on driven gear. T2 = T1 × (N2/N1) = 50 × (80/20) = 200 N·m
Answer
Driven gear speed = 250 rpm; Driven gear torque = 200 N·m
Common Gear Types and Their Characteristics
| Gear Type | Axis Orientation | Load Capacity | Noise Level | Typical Application |
|---|---|---|---|---|
| Spur Gear | Parallel | Moderate | High | Gearboxes, clocks |
| Helical Gear | Parallel | High | Low | Automobile transmissions |
| Bevel Gear | Intersecting (90°) | Moderate | Moderate | Differential drives |
| Worm Gear | Non-intersecting (90°) | Low | Low | Lifts, conveyor systems |
| Planetary Gear | Coaxial | Very High | Low | Automatic transmissions |
Interactive Tools
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Related Terms
Mechanical Bearing
A mechanical bearing is a machine element that constrains relative motion to a desired type (typically rotation or linear movement) while reducing friction between moving parts. Bearings support loads — radial (perpendicular to shaft), axial (along the shaft axis), or combined — and are critical to the longevity and efficiency of rotating machinery. They are found in electric motors, automotive wheel hubs, aerospace turbines, and virtually every machine with rotating components.
Mechanical Clutch
A mechanical clutch is a device that engages and disengages the transmission of power between two rotating shafts, allowing controlled connection and disconnection of a driver and driven component. Clutches are essential in automotive manual transmissions, industrial machinery, and any system requiring selective power coupling without stopping the prime mover. The torque transmission capacity depends on friction surface area, clamping force, and coefficient of friction between the mating surfaces.
Torque
Torque is the rotational equivalent of force — it is the tendency of a force to cause rotation about a pivot or axis. Mathematically, it is the cross product of the position vector (from the axis to the point of force application) and the force vector. Torque is essential in engineering design of engines, gears, wrenches, and any rotating machinery.
From Old Norse "gørvi" (apparel, gear) and later Middle English "gere" (equipment). The use of toothed wheels for mechanical power transmission dates to ancient Greek and Roman engineers; Hero of Alexandria (c. 10–70 AD) described gear systems in his works.