Meriam, Kraige & Bolton — Statics of Particles: Problem 2_152

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/152 The directions of rotation of the input shaft A and output shaft B of the worm-gear reducer are indicated by the curved dashed arrows. An input torque (couple) of is applied to shaft A in the direction of rotation. The output shaft B supplies a torque of to the machine which it drives (not shown). The shaft of the driven machine exerts an equal and opposite reacting torque on the output shaft of the reducer. Determine the resultant of the two couples which act on the reducer unit and calculate the direction cosine of with respect to the -axis. Problem 2/152 1. Vector representation of the input couple ● Calculation Process 1. Determine the direction of the input torque: The problem states that an input torque of is applied to shaft A in the direction of its rotation. 2. Analyze the rotation vector: Shaft A lies along the -axis. The rotation arrow shows the top of the shaft moving towards the main housing (in the negative -direction). According to the right-hand rule, a rotation that moves the top of a -axis shaft in the negative -direction corresponds to a positive rotation vector about the -axis. 3. Final Vector: ● Final Conclusion: The input couple vector acting on the reducer unit is . 2. Vector representation of the reaction couple ● Calculation Process 1. Determine the direction of rotation B: Output shaft B lies along the -axis. The rotation arrow shows the top of the shaft moving to the left (towards the housing, whic