A mechanical engineer designs a gear system where each gear has 12% more teeth than the previous. If the first gear has 40 teeth, how many teeth does the fourth gear have?

Sun, 03 May 2026 06:00:07 +0000

**How a Gear System Grows—12% More Teeth at Each Step—Explained Clearly** In industries blending precision and innovation, gear systems are essential—especially in robotics, automation, and precision manufacturing. What if each gear not only meshes with the next but also increases in size systematically? Some engineers design such systems with a measurable growth pattern: each subsequent gear has 12% more teeth than the one before. If the first gear starts with 40 teeth, how does the fourth gear perform in terms of tooth count? This question taps into a practical application of compound scaling, offering insight into mechanical efficiency, load distribution, and design innovation. Understanding gear mechanics reveals why incremental increases matter. Gears transfer motion and torque efficiently, and precise sizing affects performance and material stress. A 12% step-up in tooth count is significant—it subtly boosts strength and capacity without wild increases, balancing power transfer and mechanical durability. For engineers, this approach supports smoother operation in complex assemblies, especially as machines grow more sophisticated. ---