Velocity and Acceleration Analysis of Four-Bar Chain Mechanism
Explore the velocity and acceleration diagrams of a four-bar chain mechanism with detailed step-by-step analysis. Learn about angular velocity, angular acceleration, radial acceleration, and tangential acceleration of the chain links.
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Presentation Transcript
Velocity analysis Problem-1: PQRS is a four bar chain with link PS fixed. The lengths of the links are PQ = 62.5 mm ; QR = 175 mm ; RS = 112.5 mm and PS = 200 mm. The crank PQ rotates at 10 rad/s clockwise. Draw the velocity and acceleration diagram when angle QPS = 600 and Q and R lie on the same side of PS. Find the angular velocity and angular acceleration of links QR and RS. Step -2: Draw Velocity diagram PQ= 10 rad/s clockwise VQ= PQ x PQ Step -1: Draw Configuration Diagram with suitable scale Define scale: 200 mm = 4 inch Actual length Drawing dimension 62.5 mm 1.25 inch 175 mm 3.5 inch 112.5 mm 2.25 inch 200 mm 4 inch Link PQ Link QR Link RS Link PS = 10 x 0.0625 m Fixed Link = 0.625 m/s R VQ PQ 175mm ( 3.5 inch) R Define scale : 0.625 m/s = 2.5 inch 112.5 mm ( 2.25 inch) Q Q 900 VQ 600 PQ = 10 rad/s S P 200 mm ( 4 inch) Configuration Diagram 600 S P
Velocity analysis Step -2: Draw Velocity diagram 2.5 inch VQ= 0.625 m/s VQ PQ VQ VQ Define scale : 0.625 m/s = 2.5 inch VR RS VR/Q QR Locus of r r Direction of velocity of R p , s R VQ 900 q Q Velocity diagram 900 Perpendicular to QR. Direction of velocity Of R with respect to Q. VQ PQ = 10 rad/s 600 S P
Velocity analysis VR/S r p , s 0.625 m/s = 2.5 inch R= 1.3 inch VR/Q VQ/P q Velocity diagram pq qr pr 2.5 inch 0.625 m/s Actual length 62.5 mm 175 mm 112.5 mm 200 mm Drawing dimension 1.25 inch 3.5 inch 2.25 inch 4 inch 1.3inch 0.325 m/s Link PQ Link QR Link RS Link PS 1.66 inch 0.415 m/s QR = 1.86 rad/s QR Angular speed of link QR RS Angular speed of link RS RS = 3.69 rad/s Need for acceleration diagram
Velocity analysis VR/S r p , s 0.625 m/s = 2.5 inch VR/Q VQ/P q Velocity diagram pq qr pr 2.5 inch 0.625 m/s Actual length 62.5 mm 175 mm 112.5 mm 200 mm Drawing dimension 1.25 inch 3.5 inch 2.25 inch 4 inch 1.3inch 0.325 m/s Link PQ Link QR Link RS Link PS 1.66 inch 0.415 m/s QR = 1.86 rad/s QR Angular speed of link QR RS Angular speed of link RS RS = 3.69 rad/s Need for acceleration diagram
Acceleration analysis m/s2 m/s2 R aR/Qr aQ aR/Qr aR/Qt aR/Qt Q Angular acceleration of link RQ aQ Not Known 600 S P m/s2 aR/Qr = radial component of acceleration of R with respect to Q acting along RQ direction. Get through velocity Diagram. QR = 1.86 rad/s aR/Qt = tangential component of acceleration of R with respect to Q acting perpendicular to RQ direction. m/s2 aR/Qr aR/Q = aR/Qr + aR/Qt Define scale: 6.25 m/s2 = 1.5 inch 0.605 m/s2 = 0.145 inch aR/Qr aR/Q aQ aR/Qt aR/Qt aR/Qr aR/Qr
Acceleration analysis m/s2 m/s2 R aR/Qr aQ aR/Qr aR/Qt aR/Qt Q Angular acceleration of link RQ aQ Not Known 600 S P m/s2 Locus of r Get through velocity Diagram. QR = 1.86 rad/s m/s2 Define scale: 6.25 m/s2 = 1.5 inch aR/Qt 0.605 m/s2 = 0.145 inch aQ aQ aR/Qr aR/Qr
Acceleration analysis Locus of r aR/St R 900 aR/Sr (p , s) Locus of r aR/Sr Q r2 aR/St aR/St r aQ aQ RS aR/Qt 600 q r1 aR/St S P aR/Qr aR/Sr aR/St (p , s) aR/Qt aR/Sr Angular acceleration of link RS r2 aR/St r RQ aQ Not known to us aR/Qt q r1 aR/Qr Define scale: 6.25 m/s2 = 1.5 inch Acceleration diagram 1.52 m/s2 = 0.365 inch
