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by: Garry Goyette
Garry Goyette

GPA 3.55

D. Rocheleau

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D. Rocheleau
Class Notes
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This 2 page Class Notes was uploaded by Garry Goyette on Monday October 26, 2015. The Class Notes belongs to EMCH 332 at University of South Carolina - Columbia taught by D. Rocheleau in Fall. Since its upload, it has received 26 views. For similar materials see /class/229632/emch-332-university-of-south-carolina-columbia in Mechanical Engineering at University of South Carolina - Columbia.


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Date Created: 10/26/15
EMCH 332 Kinematics Handout4 Page 1 of2 INSTANT CENTERS OF VELOCITY Section 64 inNorton Instant Center denotes the center of rotation of a body at an instant in time The center of rotation doesn39t necessarily have to lie within the link itself It is a point in one body about which some other body is permanently or instantaneously rotating about N It is a point common to 2 bodies where the velocity ofthe two bodies are the same ie a point where there is zero relative velocity between the two bodies Example In a fourbar linkage each pin connection is an m2 instant center IC l u r W FM V Any two bodies mov1ng relative to one another have an 1nstant r 5 center I 7 To nd the instant center for a single body when the velocities of 2 points are known we take advantage of the fact that the linear velocities of all points in a rotating body are perpendicular to their radii of rotation The two points A and B along with their known velocity vectors EA and EB determine the LC If the X two velocity vectors are equal ie same magnitude 1nstant Center and direction then the LC is a point at in nity and n the body39s motion is in pure translation each instant or snap shot in time This 1s As a body moves its IC may be changing at r 39 i 7 why we call it an Instant center i of LC for a sliding body Inverse case If we know a point on the body and we know the instant center of that body s motion we can determine the direction that the body is moving Note What happens if the known location ofthe LC is a point at in nity Known LC EMCH 332 Kinematics Handout 4 Page 2 of2 IC for a rolling body The instant center for a rolling body occurs at the point of contact between the two bodies The instant center between bodies 1 and 2 is de ned as 1112 For 2 bodies moving with respect to one another there is 1 instant center For 3 bodies moving with respect to one another there are 3 instant centers Kennedy s theorem For n bodies moving with respect to one another there are nn 12 instant centers KENNEDY39S THEOREM If three bodies have plane motion relative to one another then there are three instant centers and the three instant centers all lie on the same line Using Circle Diagrams for Locating Instant Centers Locate ie identify primary instant centers EG pin connections sliding bodies and rolling bodies with no slipping 2 Draw a circle and mark evenly spaced ticks to represent each link in the mechanism 3 Draw solid lines identifying each of the known primary instant centers 4 Draw dashed lines between each point ie link to represent the remaining instant centers to be found 5 Apply Kennedy39s theorem to nd the unknown instant centers EXAMPLE Fourbar Linkage LEW chwna Notesz t m LC xed y W 4 I24 gt 39 J a H z Tim 113 lies on links A123 and MM Lima 2 124 lies on fg fm A4l2 mum


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