Graphical Analysis of a Four-Bar Mechanism

Transcription

1 Graphical nalysis of a Four-ar Mechanism Tutorial instruction: 1. lick Slide Show at the lower right corner for full screen slide show. o not click slide page 2. lick NXT when you are ready for the next step xample 2-1: etermine the angular position, angular velocity, and angular accelerations of all members of the linkage NXT

2 Graphical nalysis of Velocity Write velocity equation of Point V = V + V /, since V = 0 3. V = V + V /, since V = 0. Point = Fixed point = Point V = V / = x r / = 10 x 2.5 = 25 (in/s) 2. raw a perpendicular line of r / (use scale 25 in/s = 2.5 inch) to represent V / V = V / raw a perpendicular line of r / from fixed point (point or ) on velocity polygon 4. V = V + V /, raw a perpendicular line of r / from point on velocity polygon 5. The intersection of previous two lines is point, Fixed V = V / (2.5 inch in length NXT

3 Graphical nalysis of Velocity Measure the length of V / (green arrow) 3. Measure the length of V / (pink arrow) V / = 1.65 inch in length and convert to previous scale =1.65-inch in ( = 25 in/s), thus length V / = 16.5 in /s = 16.5 in/s 2. V / = ω 3 x r / = ω 3 x 6 (in) = 16.5 in /s ω 3 = 16.5 / 6 = 2.75 rad/s (W) = 2.69 inch in length = 26.9 in/s V / = 2.69 inch in length and convert to previous scale ( = 25 in/s), thus V =V / = 26.9 in /s 4. V / = ω 4 x r / = ω 4 x 4 (in) = 26.9 in /s ω 4 = 26.9 / 4 = 6.73 rad/s (W) V / V =V / V = V / Velocity Polygon, Fixed NXT

4 Graphical nalysis of Velocity Write velocity equation of Point V = V + V /, V / = ω 3 x r / = 2.75 x 3 = 8.25 (in/s) 2. raw a perpendicular line of r / (0.825 inch) to represent V / from point on your velocity polygon 3. Write velocity equation of Point V = V + V / V / = ω 3 x r / = 2.75 x 4 = 11.3 (in/s) raw a perpendicular line of r / (1.13 inch) to represent V / from point on velocity polygon 4. The intersection of previous two lines is point 5. raw a line from fixed point to point, and measure its length = 2.93 (in/s) Thus V = 29.3 (in/s) V =V / V V /, Fixed V = V / Velocity Polygon NXT

5 Graphical nalysis of cceleration Write acceleration equation of Point a = a + a T / + ar /, in which a = 0, α 2 = 0, a T / = α 2 x r / = 0 a = a r / = x ( x r / ) = 10 x 2.5 x2.5 = 250 (in/s 2 ) 2. raw a blue line in the opposite direction of r / (use scale 250 in/s 2 = 2.5 inch) to represent a = a r / 3. a = a + a T / + ar /, in which a = 0. Point = Fixed point = Point a = a r / = ω 4 x (ω 4 x r / ) = 6.73 x 6.73 x 4 = (in/s 2 ) (draw 1.81-inch) raw a pink line in the opposite direction of r / from fixed point (point or ) on acceleration polygon 4. a T / = α 4 x r / and is perpendicular to the direction of a r /, raw a perpendicular orange line of a r / to represent the direction of a T /, Fixed a r / a = a r / (2.5 inch in length α 2 = 0 rad/s 2 a T / NXT

6 Graphical nalysis of cceleration a = a + a T / + ar /, in which a r / = ω 3 x (ω 3 x r / ) = 2.75 x 2.75 x 6 = 45.4 (in/s 2 ) (draw inch) raw a green line in the opposite direction of r / from point on acceleration polygon 6. a T / = α 3 x r / and is perpendicular to the direction of a r /, raw a perpendicular black line of a r / to represent the direction of a T / 7. Line a T / (step 4) intersects line (step 6) at point a T / 8. onnect fixed point to point, that is a (red line),, Fixed a r / a T / a a T / a r /, Fixed a r / a = a r / (2.5 inch in length α 2 = 0 rad/s 2 a T / a r / NXT

7 Graphical nalysis of cceleration Measure the length of a (red arrow) =1.98-inch in length a =198 in/s Measure the length of a T / (lack arrow) =0.422-inch in length a T / =42.2 in/s2 11. a T / = α 3 x r / = 42.2 in/s2 α 3 x 6 = 42.2 in/s 2 α 3 = 42.2 / 6 = 7.03 (rad/s 2 ) 12. Measure the length of a T / (Orange arrow) =0.908-inch in length a T / =90.8 in/s2 13. a T / = α 4 x r / = 90.8 in/s2 α 4 x 4 = 90.8 in/s 2 α 4 = 90.8 / 4 = 22.7 (rad/s 2 ),, Fixed a r / a α 2 = 0 rad/s 2 a T / a T / a r / NXT

8 Graphical nalysis of cceleration a = a + a T / + ar /, in which a r / = ω 3 x (ω 3 x r / ) = 2.75 x 2.75 x 3 = 22.7 (in/s 2 ) (draw inch) raw a lue line in the opposite direction of r / from point on acceleration polygon 15. a T / = α 3 x r / = 7.03 x 3 = 21.9 (rad/s2 ) (draw inch) Since a T / is perpendicular to the direction of a r /, draw a perpendicular Pink line of ar / to 16. onnect fixed point to point. this is a 17. Measure the length of a = 2.4-inch a =240 in/s 2 (the answer in the text book is wrong),, Fixed represent the direction of a T / a r / a a α 2 = 0 rad/s 2 a T / a T / a T / a r / NXT N