162A 3 - Velocity

162A 3 - Velocity - 162A Introduction to Mechanisms and...

This preview shows pages 1–12. Sign up to view the full content.

162A. Introduction to Mechanisms and Mechanical Systems Chapter 3: Velocity

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Why is velocity important? square6 Mechanisms perform useful tasks square6 Velocity affects the time required to perform a given task machining of a part box2 box2 deploy or retract a classroom projector square6 Power is the product of force and velocity square6 Velocity analysis is required as a precursor to acceleration analysis
Definition of Velocity square6 In Chapter 2, we defined Displacement of a moving point P as Δ R P = R P ’ – R P The average velocity of square6 this point over a period Δ T is Δ R P / Δ T V P = square6 This is instantaneous absolute velocity

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Rotation of a Rigid Body square6 In chapter 2 box2 we saw that when a body translates, every point moves the same distance box2 When a body rotates, two arbitrarily chosen points do not undergo the same motion box2 In other words, the displacement difference, Δ R PQ , is 0 for translation and not equal to 0 for rotation. box2 Magnitude of angular velocity vector, ω,
Angular Velocity square6 Is a vector square6 Magnitude given by the above equation square6 Direction is the instantaneous axis of rotation square6 Sense of direction is obtained by the right-hand rule square6 One rigid body has only one angular velocity. In other words, if one line on the body rotates by an angle Δθ , any other line on the body also rotates the same amount Δθ. Therefore, one can select any line on the rigid body as the reference line to find the angular velocity of the body

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Pictorially,
square6 V PQ = ω x R PQ (V PQ is called the relative velocity) From , dividing both sides by Δ T and taking the limit, we get Two velocity equations which becomes square6 V P = V Q + V PQ (velocity difference equation) box2 Or, V PQ = V P - V Q box2 Relative velocity of point P w.r.t. point Q is “the absolute velocity of P minus absolute velocity of Q”

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
More on relative velocity square6 V PQ = ω x R PQ is valid only if both points are attached to the same rigid body square6 Therefore, customary to write the rigid body (e.g., 2) in the post-script, i.e., square6 V P2Q2 = ω 2 x R P2Q2
Relative velocities of points on a rigid body Relative velocity vectors: square6 V P2Q2 = ω 2 x R P2Q2 square6 V P2O2 = ω 2 x R P2O2 square6 V A2B2 = ω 2 x R A2B2 Corresponding magnitudes: square6 V P2Q2 = R P2Q2 ω 2 OR ω 2 = V P2Q2 /R P2Q2 square6 V P2O2 = R P2O2 ω 2 OR ω 2 = V P2O2 /R P2O2 square6 V A2B2 = R A2B2 ω 2 OR ω 2 = V A2B2 /R A2B2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Instantaneous Center of Velocity square6 Concept of instantaneous velocity axis for a pair of rigid bodies that move with respect to each other square6 An axis exists which is common to both bodies and about which either body can be considered rotating with respect to the other square6 In this class, we are restricted to planar motion. Each axis is perpendicular the plane of motion….so the velocity axis reduces to a center of velocity
Instantaneous Center of Velocity square6 A.k.a. Velocity Pole (in the text book), Centro (elsewhere) square6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern