One way to convert rotational motion into linear motion and vice versa is via th

Question

One way to convert rotational motion into linear motion and vice versa is via the use of a mechanism called the Scotch yoke, which consists of a crankC that is connected to a slider B via a pinA. The pin rotates with the crank while sliding within the yoke, which, in turn, rigidly translates with the slider. This mechanism has been used, for example, to control the opening and closing of valves in pipelines. Letting the radius of the crank boR = 28 cm, determine the angular velocity to omega c and the angular acceleration ac of the crank at the instant shown if Theta = 26degree and the slider is moving to the right with a constant speed vB = 45 m/s. omega C = k rad/s Theta = Times 10 rad/s2 k. From the perspective of crank C, the velocity and acceleration of A are naturally described in radial and circumferential directions as defined by Theta. Letting O be the fixed bearing about which the crank rotates, v A = omega C Times r A/O aA = alpha C Times r A/O = omega2r A/O. These entities can then be resolved into horizontal and vertical components. Matching the horizontal components of A to the motion of slider B provides the constraints required to obtain the angular velocity and angular acceleration of the crank.

Explanation / Answer

d2()/dt2 = .. =

i am assuming C = x k rad/s

& C = y k rad/s2

rA/O = -rcos i + r sin j = - 0.252i + 0.123 j m

vA =   C * rA/O = x k * (- 0.252i + 0.123 j ) = -0.252 x j - 0.123 x i m/s

Since horizontal component of A and slider will be equal hence

  - 0.123 x i = 45 => x = - 365.854

aA = C * rA/O - 2 *  rA/O = y k * (- 0.252i + 0.123 j ) - 133849.149 * (- 0.252i + 0.123 j )

= (33729.986 - .123 y ) i - (16463 .445 + 0.123 y) j

Comparing horizontal acceleration

33729.986 - .123 y = 0 => y = 2.742 *105

So answers are

C = -365.854 k rad/s

C = 2.742*105 k rad/s2

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.