Question

Question 3. A crank shaft mechanism is shown in Figure 3. Link B is rotating with a constant angular velocity wgåg in the fixed reference frame A as shown in the figure. For this mechanism: (a) Using the vector kinematic equations and methods taught in this [20 marks) module, obtain the expressions for velocity and acceleration of point in the fixed frame A, in terms of wb.lg, lc, and e.

Answer 1

The cosine law is used to establish relation between the length of links and the length OQ. The cosine law is an quadratic equation, the solution of this equation will give the length OQ. OQ is represented as s. Once s is obtained, the first derivative of the s will give us the velocity of the slider and the second derivative will give us the acceleration of the slider.

(do / dt) =w © 0 S 09?+ OP?- 200) 0P) Cos 0 = QP2 < (Law of losine) Let OQ=6 s+ 4² - 2212 los o = 4² A = al Case + / 1 car ²0 - 4 + 4 + Con Solving the quadratic Equ) s = 4 Cose + 2 2 4 - 4 Sin²o velocity of Pennt a 6=(08/0) ul = -bySin o (deldt) + Sin o " 2sin oloso (1976) 2 U = - L3 Sino wa v Sin 20 w 2 4 ² - 4 Sin²o Y = -lo Shot 2 Sin 20 26 - 4 Sin²o 2 Acceleration of Point a 9 = ): id's = a la loxo (do (de) - 1 Cor 28 (delat) z le? Sin 20. (2 Site O bs ) (do/dt) 2/2² - La sinto 4 (16 ² - 4 Sino a = -12 los o. w? – 4 los 20 w2 16² (Sin 20² w² 14² - 16 Sino 4 (16² - 4 Sin ²012 a = -40² / los o + 4 Curs 20 18 (Sin 20) 4 (4²-43 Sin 20) 3/2 + 2 re 16 - 18 Sin ²0