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Notes_03_05

# Notes_03_05 - Notes_03_05 page 1 of 7 Instantaneous Centers...

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Notes_03_05 page 1 of 7 Instantaneous Centers Instant center - unique point at which two objects in general planar motion have the same velocity Absolute center – instant center between an object and ground Relative center – instant center between two moving objects Velocity of a point – tangent to the path of the point, perpendicular to the line that joins the point and the relative instant center of rotation Kennedy-Aronhold theorem – relative instant centers between three bodies are collinear J1 joints define instant centers 1,2 and 2,3 are collinear with 1,3 1,4 and 3,4 are collinear with 1,3 1,2 and 1,4 are collinear with 2,4 2,3 and 3,4 are collinear with 2,4 4 1 1,4 3 2 2,3 6 5 5,6 at ∞ 1 7 1,7 at ∞ no slip V = r ϖ 8 1 1,8 1 2 3 4 from J1 joints by Kennedy- Aronhold A B D 2 3 4 C 1,3 2,4

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Notes_03_05 page 2 of 7 Velocity Transfer V B2 = ϖ 2 (AB) V B2 = V B3 V B3 = ϖ 3 (BP) V C3 = ϖ 3 (CP) V C3 = V C4 V C4 = ϖ 4 (CD) V Q2 = ϖ 2 (AQ) V Q2 = V Q4 V Q4 = ϖ 4 (DQ) 2 3 Q ≡ 2,4 P ≡ 1,3 A B D 4 C ϖ 2 P ≡ 1,3 A B 2 V B2 B 3 V B3 ϖ 2 ϖ 3 D 4 C
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