Homework5bsol.spring11

Homework5bsol.spring11 - ME 352 - Machine Design I Spring...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 352 - Machine Design I Name of Student__ _________________________ Spring Semester 2011 Lab Section Number ________________________ Homework No. 5 (30 points). Due at the beginning of lecture on Monday, February 21st. Consider the sliding-block linkage shown in Example 2.5, Figure 2.24, page 77, and repeated here as Figure 1. The length of the ground link is 14 2 RO O9 i n c h e s = = and the length of link 2 is 22 A 4 . 5 i n c h e s . == The position solution for the input angle o 2 135 θ= can be obtained from trigonometry and the answers are 34 4 R O A 12.59 inches = = and . o 3 434 104.64 The angular velocity and the angular acceleration of the input link 2 are 2 5krad s ω=− / and 2 2 10 k rad s , α= / respectively. The length of link 4 is 4 OC 2 0 i n c h e s = and note that the origin of the XY reference frame is now chosen to be coincident with the ground pin O 2 , see Figure 1. Part A. Use the vector loop approach to determine the first-order and the second-order kinematic coefficients of this linkage in the given position. Part B. Using the method of kinematic coefficients determine: (i) the relative velocity and acceleration between links 3 and 4 (denote as 34 R ± and 34 R ±± ). (ii) the angular velocity and acceleration of link 4. Give the magnitudes and the directions. (iii) the velocity and acceleration of point C. Give the magnitudes and the directions. (iv) the unit tangent and normal vectors to the path of point C. Show the directions of these vectors on a figure. (v) the radius of curvature of the path of point C. (vi) the X and Y coordinates of the center of curvature of the path of point C. Figure 1. The Sliding-Block Linkage.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Solution to Homework Set 5. Part A. A suitable set of vectors for the sliding-block linkage are shown in Figure 2. Figure 2. The vectors for the sliding-block linkage. The vector loop equation (VLE) for the linkage is ?? 0 123 4 I RRR √√ + −= (1) The X and Y components of Equation (1) are 11 2 2 3 4 3 4 cos cos cos 0 RR R θ θθ + (2a) and 3 4 sin sin sin 0 R + (2b) Differentiating Equations (2) with respect to the input angle θ 2 gives 2 2 34 34 34 34 34 sin sin cos 0 R −+ = (3a) and 2 2 34 34 34 34 34 cos cos sin 0 R (3b)
Background image of page 2
3 Equations (3) can be written in matrix form as 34 34 34 34 22 34 34 34 34 sin θ cos θθ sin θ cos θ sin θ R cos θ R R R R ⎡⎤ = ⎢⎥ −− ⎣⎦ (4) The determinant of the coefficient matrix is 34 34 34 34 34 34 34 34 34 34 34 sin θ cos θ sin θ cos θ cos θ sin θ R DET R R R R == = (5) Using Cramer’s rule, the first-order kinematic coefficient for link 3 can be written as 3 4 3 4 2 2 34 2 2 34 34 34 sin cos cos sin sin sin cos cos R R RR DET R θ (6a) which can be written as 3 4 34 34 cos ( ) R R ′ = (6b) The first-order kinematic coefficient for links 3 and 4 can be written as 34 34 2 2 34 34 2 2 2 34 2 34 2 34 2 34 34 34 sin sin cos cos cos sin sin cos R DET R −+ (7a) which can be written as 23 4
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/23/2011 for the course ME 352 taught by Professor Staff during the Spring '08 term at Purdue University.

Page1 / 9

Homework5bsol.spring11 - ME 352 - Machine Design I Spring...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online