User:Pushkar Kamble

Aronhold-Kennedy's theorem: Statement: If three links have relative motion with respect to each other, their relative instantaneous centres must lie on a straight line.

Imagine a triangle ABC, AB being base. Base AB being fixed link, other two sides AC and BC represent two distinct links. They are pinned at base and at upper vertex. Now if we assign this mechanism its ICR's. They will be like I_12 and I _13 located at A and C respectively. Subsequently I_23 will be at B. Now if we consider, B lies on link AB then its velocity must be perpendicular to link AB. But if we consider point B is on link BC then its velocity must be perpendicular to link BC. It seems conflicting that one point having velocities in different directions at same time, well, this doesn't conflict when we say point B lies on base AB. This confirms to Aronhold-Kennedy's theorem, proving ICRs are collinear.