According to Kennedy’s theorem, where do the instantaneous centers of three mutually moving bodies lie___________________?
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Answer: D. a straight line
Explanation
Kennedy's theorem states that three bodies in relative motion have three instantaneous centers. Geometric analysis proves that these three distinct instantaneous centers must always be collinear. This theorem simplifies velocity analysis in complex multi-bar mechanisms and linkages. An instantaneous center represents a point where relative velocity between two bodies is zero. Kinematics relies on graphical theorems to determine velocities without complex calculus equations. Sir Alexander Kennedy contributed foundational principles to the science of mechanism kinematics.
Automotive steering geometry analysis frequently utilizes instantaneous centers to check alignment. Mechanism designers apply Kennedy's theorem to verify velocity ratios across complicated linkages. Graphical velocity polygons and centrodes help visualize machine component interactions clearly. A triangle describes the layout of three bodies but their centers lie on a single line. A single point would imply all three bodies share identical motion characteristics instantly. Curved paths are incorrect because instantaneous centers form straight collinear geometric lines.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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