A mechanism consists of two rigid straight links AC and DO, rotating about C and O...

  

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A mechanism consists of two rigid straight links AC and DO, rotating about C and O respectively, and connected by a pin-slider (where the pin is attached to link AC at point A, and slides in a slot on link DO). Link DO has constant angular velocity, and point B is a point halfway along link DO, coincident with point A at the instant considered. Velocity and acceleration diagrams for the mechanism are shown below. Point B is used as the reference point for the r- coordinates, with r in the direction of the slot on DO. (a) Calculate the angle ß shown on the velocity diagram, and the velocity of point B (m/s). (b) Calculate the lengths (in m) and angular velocities (in rad/s, including direction) of links AC and DO, using the velocities and normal components of acceleration for points A and B. (c) Calculate the theta component of aAIB. (Hint: By using B as the r- reference point, the radius r to point A is zero in r-0 formulae.) Hence, use the acceleration diagram to determine the angular acceleration of link AC (in rad/s², including direction). (d) Draw a diagram of the mechanism, showing all lengths and angles. AB to VA VAB ав P a 0.900 m/s 0.6364 m/s 1.273 m/s² 3.60 m/s² 8p 45° BAD BA ав 45° BAB, ªд³е (Try it first before reading the below.) Solution notes: (d) A diagram should be useful for solving. As you read through the question, draw little sketches representing each addition to your knowledge of the physical mechanism, then bring it together when you can. Except for lengths, the mechanism can be completely drawn from the information in the paragraph plus the direction information in the diagrams, before you do any calculations. (a) should be very easy. (b) is asking for r and to values, using velocities and normal accelerations. How are they connected? (c) Use r-theta formulae, noting the standard "hint" for sliding, then use the geometry of the acceleration diagram to find the tangential component of aA. A mechanism consists of two rigid straight links AC and DO, rotating about C and O respectively, and connected by a pin-slider (where the pin is attached to link AC at point A, and slides in a slot on link DO). Link DO has constant angular velocity, and point B is a point halfway along link DO, coincident with point A at the instant considered. Velocity and acceleration diagrams for the mechanism are shown below. Point B is used as the reference point for the r- coordinates, with r in the direction of the slot on DO. (a) Calculate the angle ß shown on the velocity diagram, and the velocity of point B (m/s). (b) Calculate the lengths (in m) and angular velocities (in rad/s, including direction) of links AC and DO, using the velocities and normal components of acceleration for points A and B. (c) Calculate the theta component of aAIB. (Hint: By using B as the r- reference point, the radius r to point A is zero in r-0 formulae.) Hence, use the acceleration diagram to determine the angular acceleration of link AC (in rad/s², including direction). (d) Draw a diagram of the mechanism, showing all lengths and angles. AB to VA VAB ав P a 0.900 m/s 0.6364 m/s 1.273 m/s² 3.60 m/s² 8p 45° BAD BA ав 45° BAB, ªд³е (Try it first before reading the below.) Solution notes: (d) A diagram should be useful for solving. As you read through the question, draw little sketches representing each addition to your knowledge of the physical mechanism, then bring it together when you can. Except for lengths, the mechanism can be completely drawn from the information in the paragraph plus the direction information in the diagrams, before you do any calculations. (a) should be very easy. (b) is asking for r and to values, using velocities and normal accelerations. How are they connected? (c) Use r-theta formulae, noting the standard "hint" for sliding, then use the geometry of the acceleration diagram to find the tangential component of aA.