Lecture_06 - part of a four-bar loop that contains the...

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Kinematics and Dynamics Kinematics and Dynamics of Machines of Machines ENGR 3270U ENGR 3270U Lecture 6 Lecture 6 Yuping He University of Ontario Institute of Technology September 24, 2008
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1.2 2.5 The Acceleration Image Theorem Objective: To obtain accelerations of additional points on a rigid body when the accelerations of two points are already known. Theorem If PQR is a trainagle fixed in a rigid body in motion relative to the fixed frame, the triangle p’q’r’ in the acceleration diagram is similar to triangle PQR. Triangle p’q’r’ is magnified by a factor that is a function of and and is rotated from PQR by an angle that is also a function of and . α ϖ ϖ α
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1.3 Example: Given the dimensions of the linkage shown in the following figure, find and if rpm CW and . c a 6 α 60 2 = ϖ 0 2 = α 1) Position Analysis 2) Velocity Analysis 3) Acceleration Analysis t F E r F E F E t D E r D E D E a a a a a a a a 6 6 6 6 6 6 5 5 5 5 5 5 / / / / + + = = + + =
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1.4 2.6 Solution by Inversion Problem: If in a linkage where the driver link is not
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Unformatted text preview: part of a four-bar loop that contains the frame as one of the members, it is not possible to analyze the linkage directly using the vector polygon approach. Solution: If the position of the linkage is known, a velocity solution can be achieved recognizing that all of the velocities in the linkage are linearly related to the velocity of the input member. Therefore, we can solve the velocity problem indirectly by first assuming the linkage to be driven by , rotating at 1 rad/ s in a specified direction. The velocity polygon is completed and the angular velocity of is found. C O C A O A 1.5 Example: 1) Position Analysis a) Changing AO A continuously to get the coupler’s curve b) With the given O C C position, getting the required linkage position. 2) Velocity Analysis 1.6 2) Velocity Analysis...
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