Instant centers of velocity Section 3 13 Instant

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: I 12 Link 1 (ground) Instant center, I 12 1 (ground) 1

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

Rules for finding instant centers Sliding body on curved surface Sliding body on flat surface 2 2 1 1 I 12 is at infinity I 12 Rolling wheel (no slip) Sliding bodies common normal 2 I 12 (point of contact) 3 I 23 Common tangent (axis of slip) 3

Link is pivoting about the instant center of this link and the ground link I 13 Link 3 rotates about instant center I 13 3 1 4

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, 5

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

Instant centers of four-bar linkage I 13 3 I 34 I 23 I 24 4 2 I 14 I 12 1 7

Velocity analysis using instant centers (Section 3. 16) Problem: I 13 Know 2 Find 3 and 4 3 2 2 3 B 4 A 4 I 12 1 8

Velocity analysis using instant centers (continued) Steps 1. Find VA, normal to O 2 A, magnitude= 2(O 2 A) 2. Find 3=length of VA/ (I 13 A) 3. Find VB, normal to O 4 B, magnitude= 3(I 13 B) 4. Find 4=length of VB/ (O 4 B) 9

Velocity ratio (Section 3. 17) B A 3 4 4 2 O 4 1 10