Kinematics of Mechanisms 6 Acceleration

Transcription

1 Kinematics of Mechanisms 6 Acceleration Latifah Nurahmi Latifah.nurahmi@gmail.com Room C.250 Acceleration analysis Acceleration analysis: Determine the manner in which certain points on the mechanism are either speeding up or slowing down. Kinematics of Mechanisms by Latifah Nurahmi 2 1

2 Linear acceleration Linear acceleration A = rate of change in linear velocity Because: Kinematics of Mechanisms by Latifah Nurahmi 3 Angular acceleration Angular acceleration = rate of change in angular velocity Because: Kinematics of Mechanisms by Latifah Nurahmi 4 2

3 Assignment 1 The grinding wheel will speed up to 1800 rpm in 2s when the motor is tuned on. Assuming that the speed up is at constant rate, determine: - Angular acceleration - Angular displacement from intial. Kinematics of Mechanisms by Latifah Nurahmi 5 Assignment 1 In constant acceleration, we determine: Kinematics of Mechanisms by Latifah Nurahmi 6 3

4 Assignment 1 Kinematics of Mechanisms by Latifah Nurahmi 7 Acceleration of general points Velocity of points moving in general fashion, may change in 2 ways: The magnitude of velocity changes. It produces acceleration along the path, named tangential acceleration A t. The direction of velocity changes. It produces centrifugal acceleration, perpendicular to the path, named normal acceleration A n. Kinematics of Mechanisms by Latifah Nurahmi 8 4

5 Acceleration in pure rotation A PA A t PA P Length of link: p, A n PA Magnitude of tangential acceleration A t = p A Magnitude of normal acceleration A n = p 2 Kinematics of Mechanisms by Latifah Nurahmi 9 Acceleration Analysis of Four-Bar Mechanism Kinematics of Mechanisms by Latifah Nurahmi 10 5

6 Four bar mechanism Velocity loop equation Let us recall: Derive w.r.t time: Kinematics of Mechanisms by Latifah Nurahmi 11 Four bar mechanism Solution: Given value of θ and θ, find φ and ψ Then find φ φ = a sin ψ θ h sin ψ φ θ Then find ψ ψ = a sin φ θ b sin φ ψ θ Kinematics of Mechanisms by Latifah Nurahmi 12 6

7 Four bar mechanism Acceleration loop equation Derived again w.r.t time Tangential acceleration A t Normal acceleration A n Tangential acceleration A t Normal acceleration A n Tangential acceleration A t Normal acceleration A n Kinematics of Mechanisms by Latifah Nurahmi 13 Assignment 2 The mechanism shown below, is used in a distribution center to push boxes along a platform. The input link is driven by an electric motor with angular velocity 25 rad/s and accelerates at a rate of 500rad/s 2. Determine: 1. The instantaneous acceleration at the end of the input link! 2. The angular accelerations of coupler and rocker! Kinematics of Mechanisms by Latifah Nurahmi 14 7

8 Assignment 2 1. The instantaneous acceleration at the end of the input link, point A y A n A t x Kinematics of Mechanisms by Latifah Nurahmi 15 Assignment 2 2. The angular accelerations of coupler and rocker, link 3 and link 4 φ y ψ x Kinematics of Mechanisms by Latifah Nurahmi 16 8

9 Assignment 2 Steps to solve: 1. Find the coupler angle and rocker angle (φ and ψ). 2. Derive the position loop vector 3. Derive the velocity loop vector 4. Solve coupler velocity and rocker velocity ( φ and ψ). 5. Derive the acceleration loop vector 6. Solve coupler acceleration and rocker accelerations ( φ and ψ). y x Kinematics of Mechanisms by Latifah Nurahmi 17 Relative acceleration A t PA A PA, P A n PA Point A belongs to the slider and the link Point A has absolute acceleration VA. Point A has relative acceleration w.r.t point P A VA AA Kinematics of Mechanisms by Latifah Nurahmi 18 9

10 Acceleration Analysis of Slider Crank Mechanism Kinematics of Mechanisms by Latifah Nurahmi 19 Slider crank mechanism Velocity loop equation Let us recall: Derive w.r.t time: Kinematics of Mechanisms by Latifah Nurahmi 20 10

11 Slider crank mechanism Solution: Given value of φ and θ, find s Then find s s = a θ sin(φ θ) cos φ Then find θ θ = s cos φ a sin(φ θ) Kinematics of Mechanisms by Latifah Nurahmi 21 Slider crank mechanism Acceleration loop equation Derived again w.r.t time Tangential acceleration A t Normal acceleration A n Tangential acceleration A t Normal acceleration A n Tangential acceleration A t Kinematics of Mechanisms by Latifah Nurahmi 22 11

12 Slider crank mechanism Acceleration loop equation Derived again w.r.t time Relative acceleration Kinematics of Mechanisms by Latifah Nurahmi 23 Assignment 3 The figure shows a hackshaw. The lectric motor drives the free end of the motor crank (point B) at a velocity of 12 in/s. The crank is accelerating at a rate of 37 rad/s2. The saw move to the left with velocity 9.8 in/s and is accelerating at a rate of 82 in/s2. Determine the relative acceleration of point C w.r.t point B. Kinematics of Mechanisms by Latifah Nurahmi 24 12

13 Assignment 3 Kinematics of Mechanisms by Latifah Nurahmi 25 13