Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_109

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The pruning mechanism of a pole saw is shown as it cuts a branch . For the particular position drawn, the actuating cord is parallel to the pole and carries a tension of . Determine the shearing force applied to the branch by the cutter and the total force supported by the pin at . The force exerted by the light return spring at is small and may be neglected. Given: , , , . Problem 4/109 (a) Shearing force applied to the branch ● Calculation Process 1. Present Final Formula: Based on the geometry of the mechanism, the cutter is in equilibrium under the forces from the cord, the two links and , and the branch reaction. Since and , the linkage is a parallelogram. In this configuration, links and are parallel. Let be the angle of these links relative to the pole. Summing forces perpendicular to the links for the cutter rigid body (where link reactions have no component) gives: where is the angle between the cord and the links, and is the angle between the shearing force and the direction perpendicular to the links. 2. Substitute Values: From the diagram, the cord is parallel to the pole. The angles relative to the pole direction are: , , and (assuming consecutive arcs). - Tension is parallel to the pole. - Links and are at . The angle . - The blade direction is along at . Assuming the shearing force is perpendicular to the blade, its angle is . - The direction perpendicular to the links is . - The angle . S 30 lb P EC =AB1 ′′ =BC=ED3