The lever is attached to the shaft A using a key that has a...

The lever is attached to the shaft $A$ using a key that has a width $d$ and length of $25 \mathrm{mm}$. If the shaft is fixed and a vertical force of $200 \mathrm{N}$ is applied perpendicular to the handle, determine the dimension $d$ if the allowable shear stress for the key is $\tau_{\text {allow }}=35 \mathrm{MPa}$

Key Concepts

Shear Stress

Shear stress is a measure of force per unit area acting parallel to the plane of interest. In mechanical design, it is calculated by dividing the applied force by the cross-sectional area over which the force is distributed. This concept is essential when evaluating whether a component such as a key in a shaft-key connection can sustain the applied loads without failing.

Allowable Shear Stress

Allowable shear stress refers to the maximum shear stress that a material is permitted to experience under load without risking failure. It is a critical design parameter used to ensure that the material remains within safe stress limits during operation, thereby preventing premature failure of the component.

Key and Keyway Design

Keys and keyways are fundamental mechanical design elements used to connect rotating components, allowing for the transmission of torque between a shaft and a hub or lever. Proper key design involves determining dimensions that can handle the applied forces without exceeding the material’s allowable shear stress, ensuring reliable load transmission and structural integrity.

Lever Mechanics

Lever mechanics involves the study of how forces applied at a distance from a pivot generate moments (or torques) that can amplify or modify the effect of the applied force. In the context of key design, understanding how a force applied to a lever translates into stress on a connecting key is important for ensuring that the dimensions of the key are adequate for safe operation.

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