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Instant centers of velocity (Section 3.13)

This section explains instant centers, which are points in a plane where a link can be thought to rotate relative to another link. These centers are found using rules and can help in velocity analysis. Learn how to find instant centers and analyze velocities using instant centers.

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Instant centers of velocity (Section 3.13)

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  1. Instant centers of velocity (Section 3.13) Instant center - point in the plane about which a link can be thought to rotate relative to another link (this link can be the ground) An instant center is either (a) a pin point or a (b) two points - - one for each body -- whose positions coincide and have same velocities. 2 2 Instant center, I12 Instant center: I12 1 (ground) Link 1 (ground)

  2. Finding instant centers • By inspection (e.g. a pinned joint is an instant center) • Using rules • Aronhold-Kennedy rule

  3. Rules for finding instant centers Sliding body on curved surface Sliding body on flat surface 2 2 1 1 I12 is at infinity I12 Rolling wheel (no slip) Sliding bodies common normal 3 2 I23 I12 (point of contact) Common tangent (axis of slip)

  4. Link is pivoting about the instant center of this link and the ground link I13 3 Link 3 rotates about instant center I13 1

  5. For each pair of links we have an instant center. Number of centers of rotation is the number of all possible combinations of pairs of objects from a pool of n objects,

  6. Aronhold-Kennedy rule • Any three bodies have three instant centers that are colinear

  7. Instant centers of four-bar linkage I13 3 I34 I23 I24 4 2 I14 I12 1

  8. Velocity analysis using instant centers (Section 3.16) Problem: Know 2 Find 3 and 4 I13 3 B 3 4 A 4 2 2 I14 I12 1

  9. Velocity analysis using instant centers (continued) Steps • Find VA, normal to O2A, magnitude= 2(O2A) • Find 3=length of VA/ (I13A) • Find VB, normal to O4B, magnitude= 3(I13B) • Find 4=length of VB/ (O4B)

  10. Velocity ratio (Section 3.17) B A 3 4 4 2 O2 O4 1

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