How To Design A Crankrocker

Transcription

1 Graphical Linkage Synthesis Lecture 5

2 Time ratio The timing of the crank-rocker can be assessed using the two stationary positions. Time ratio = OR Time ratio = Time it takes to complete forward motion/ Time it takes to complete return motion Crank angle to complete forward motion/ Crank angle to complete return motion

3 Time ratio and return mechanisms Even return crank-rocker For a given constant input speed, It takes the same time to complete the forward and the return motion, therefore: Time ratio =1 The two stationary positions of the crank line up with each other, and the angles swept between these stationary positions are equal.

4 Time ratio and the return mechanisms Quick-return crank-rocker For a given constant input speed, the Time it takes to complete the forward motion is more than the time it takes to complete the return motion, therefore: Time ratio >1 The two stationary positions of the crank do not line up with each other, and the angles swept between the stationary positions are not equal.

5 Time ratio and geometry of QRM Quick-return crank-rocker α + β =360 Time ratio: T R = α/β δ = α = β Or the time ratio is: T R = (180 + δ)/(180 - δ) These angular values and relationships will be used to synthesize the linkage.

6 Transmission Angle Transmission angle, μ: Angle between the coupler link and the output link. μ =θ 4 θ 3 As the input link 2 rotates, all of the angles change. Therefore you can plot μ as a function of input angle θ 2.

7 Min. and Max.Transmission Angle Max. transmission angle µ Min. transmission angle Minimum and maximum transmission angle occur when link 2 (crank) becomes collinear with link 1 (ground link)

8 Transmission Angle and Efficiency Transmission angle of a crank-rocker gives an indication of the efficiency of power transmission from the input to the output link. At μ = 90 o all of the force from the coupler link is being transmitted to the output link to produce the maximum output torque. μ = 90 o gives maximum efficiency (torque transmission). In practice, μ = [40,140 ] is preferred.

9 Design of a CR Quick-return Mechanism Design a Grashof four-bar, crank-rocker, quickreturn mechanism with the following requirements: The mechanism will have: 1) a time ratio of ) an output rocker angle of 50. while maintaining a transmission angle between 40 and 140, and, 3) must fit and operate within a design space of 8 x 11 inches.

10 Design Solution Step 1: Draw the output link in both extreme positions (pivot O4, end positions B1 and B2). Step 2: Draw a construction line through B1 at any convenient angle. Note: The orientation of the line drawn in Step 2 is arbitrary and an iterative trial and error process will have to be employed for making design corrections, if necessary.

11 Design Solution Step 3: Calculate δ using the given time ratio equation. Step 4: Draw a construction line through B 2 at an angle of δ. Step 5: Label the intersection point O 2.

12 Design Solution Step 6: The line O 2 O 4 now defines the ground link. Step 7: Locate point C on the extension of O 2 B 2 so that O 2 C = O 2 B 1

13 Design Solution Step 8: Determine the length of the crank by Measuring length B 2 C, and solving for Link 2 = r 2 = (B 2 C) /2 Step 9: Calculate the lengths of the coupler: length of link 3, r 3 = O 2 B 1 r 2

14 Design Solution Step 10: Check if Grashof s condition is satisfied. If non-grashof, repeat steps 3 to 8 with O 2 further from O 4. Step 11: Check the transmission angles. Note: to promote smooth running and good force transmission, μ = [40,140] degrees

15 Design Conclusion and Specifications Step 12: Specify the mechanism: - List the link lengths. Label the links. - Draw the mechanism in at least one position. Ground link, R1 = Input link, R2 = Coupler link, R3 = Output link, R4 =