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Two kinematics exercises involving the determination of acceleration and velocity of points in a two-cylinder air compressor and a moving rectangular plate. The exercises involve applying kinematic principles to calculate the velocity and acceleration of different points on the mechanisms. Detailed solutions with diagrams and step-by-step calculations, making it a valuable resource for students studying kinematics and mechanics.
Typology: Exercises
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1. En el compresor de aire con dos cilindros que se muestra en la figura las bielas BD y BE tienen una longitud de 190mm y la manivela AB gira alrededor del punto fijo A con una velocidad angular constante de 1500 rpm en el sentido de las manecillas del reloj. Determine la aceleración de cada pistón cuando ө=0. - Diagrama cinemático Conversión E D B A VE VB VD ˠ Datos Longitud de las bielas BD y BE 190 mm Velocidad angular del punto A 150 rpm
1 min
2 π Rad
= 157 , 08 rad /s Como el punto A es fijo: VA=0, Aa= 0
2
aB=(0.05)(157.08)² ⦟ 45 ° aB=1233.7 m/s 2 ⦟ 45 °
VB=0.75i+( ω
k)( 1.5 sen ө −1.5 cos ө ) VBj=0.75 i+1.5 sen ω ө
j−1.5 cos ω ө
i Se agrupan las i=i y j=j 0 =0.75−1.5 cos ω ө
ω
1.5 cos ө VB=1.5 sen ω ө
VB=Tan x ө 0.
VD=0.75 i+
1.5 cos ө k
x (0.5 cos i ө −0.5 sen j ө ) 2 1 X Y 0.5 m
