Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ME 481 - H06 Name ________________________ Use generalized coordinates {q} and joint constraints {} for the slider crank shown below. x 2 y 2 r 2 2 2 x 3 r q y 3 3 3 3 r4 x 4 4 y 4 4 r2 A r1 A B B r3 r2 C C r4 r3 4 y4 2 2 t B G3 3 2 AB = R = 0.985 inch BC = L = 4.33 inch BG3 = 1.1 inch G2 is at A2 (balanced crank) G3 is on centerline of link 3 G4 is at C4 (simple piston model) x2 axis along centerline of link 2 x3 axis along centerline of link 3 2 = 1000 rpm CCW constant C 4 A B3 y3 x3 B2 y2 x2 C3 G3 y4 A2 y1 A1 s 2 ' A 0 0 0 s 4 ' C 0 C4 x4 x1 s 2 ' B r1 A R 0 0 0 example for B3 BLUEPRINT INFORMATION BG 3 L BG 3 s 3 ' B s 3 ' C 0 0 r3 B r3 A 3 s 3 ' B cos 3 A 3 sin 3 sin 3 cos 3 ME 481 - H06 Name ________________________ 1) Evaluate residuals {} for rough estimates of generalized coordinates {q} at t = 0.005 sec shown below. Comment on the relative precision of {} versus {q}. 0 inch _______________ _______________ 0 inch 0.4363 rad (25) _______________ 2.0 inch _______________ q _______________ 0.5 inch 0.1745 rad (10) _______________ 5.0 inch _______________ 0 inch _______________ _______________ 0 rad (0) 2) Use geometric equations to determine better estimates for {q} at time t = 0.005 sec. Then evaluate new residuals. Comment on precision of {q} and {} between parts 1) and 2). 0 inch _______________ _______________ 0 inch 2 t __________ _______________ _______________ _______________ q _______________ _______________ _______________ _______________ _______________ _______________ 0 inch _______________ _______________ 0 rad (0) 3) Evaluate the Jacobian q for your better estimate of {q} at t = 0.005 sec. q ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ME 481 - H06 Name ________________________ 4) Use your code to perform a Newton-Raphson position solution at t = 0.010 sec. Calculate piston position x4 and determinant of the Jacobian. Validate with geometric equations. x4 (Newton-Raphson) ____________ det q ____________ x4 (geometric) ____________ 5) Compute piston velocity x 4 and acceleration x 4 at t = 0.010 sec using a matrix solution with right-hand-side (RHS) vectors and . Validate with geometric equations. x 4 (matrix) ____________ x 4 (geometric) ____________ x 4 (matrix) ____________ x 4 (geometric) ____________ EXTRA CREDIT Place a loop around your solution for part 5) using 0 ≤ t ≤ 0.06 sec and provide MATLAB graphs for piston position x 4 , velocity x 4 and acceleration x 4 as functions of crank angle 2 . Validate using results from geometric equations on the same MATLAB graphs. EXTRA EXTRA CREDIT Modify your slider crank code for part 5) to analyze the four bar in Notes_04_05. This should only require modifying the last three rows in your constraint vector, your Jacobian matrix and your acceleration RHS vector. use 2 = 65° 2 = 10 rad/sec CW = 2 rad/sec2 CCW 2 validation 3 = 13.151° 3 = _______________ = +7.0627 rad/sec2 3 4 = -65.173° 4 = -5.3533 rad/sec = _______________ 4