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# Tutorial ME3112

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This 10 page Study Guide was uploaded by Raja on Saturday November 21, 2015. The Study Guide belongs to ME3112 at National University of Singapore taught by Prof Lim Kian Meng in Fall 2015. Since its upload, it has received 164 views. For similar materials see Mechanics of Machines in Mechanical Engineering at National University of Singapore.

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Date Created: 11/21/15

ME31 12 Mechanics of Machines G Leng Text F Beer E Johnston and P Cromwell quotVector Mechanics for Engineers Dynamics Ninth Edition in SI unitsquot 2010 McGraW Hill Course Website httpdynlabmpenusedusgmpelsb Level I Particle kinematics Fixed and translating frames 1 J K Chapter 11 9 to 1112 1190 The motion of a particle is defined by the equations x 2 cos wt 4151 y 1 4 cos 2771 where x and y are expressed in meters l t is expressed in seconds Show that the path of the particle 2 part of the parabola shown and determine the Velocity and the 5 neeleration when a t 0 b t 15 s glmuk J 2 I Ans a0ms 27l392 I 167t2J ms2 Mme b 2x I ms 46an ms2 3 I U 11170 5 Pin P is attached to BC and slides Freely in the slot of 0A Deter mine the rate of change 0 of the angle 0 knowing that BC moves at a constant speed 1 Express your answer in terms of it h g and 6 J Ans 0 V0h secB sin2B 0 Level II Particle kinematics Rotating reference frame i j k Chapter 1510 to 1511 15160 At the instant shown the length of the boom AB is being dgcreasg ii at the constant rate of 02 ms and the boom is being lowered a constant rate of 008 rads Determine a the velocity of poiri B b the acceleration of point B Ans a 02i 048j ms b 0038i 0032j ms2 ME3112 Mechanics of Machines 15175 15176 Knowing that at the instant shown the rod attached at B rotates with a constant counter clockwise angular velocity of 6 rads determine the angular velocity and angular acceleration of the rod attached at A Fig Pisi75 i Ans 15 krads 779 kradsz Fig P15l76 Ans 6 k rads 6235 k rads2 Level III Rigid body kinematics Chapter 151 to 159 1540 In the engine system shown thc crank AB has a constant clockni isc angular 39lcity39 of 2000 1pm For the crank position indicatcrl lt39lt i39lllllle a the angular velocity of thc connecting rod BI b tlic u39locity ol39 the piston P 39 Ans a 62K rads b 131 I ms 1 900 mm ire 15125 and 15126 Knowing that crank AB rotates about point will in Mali an angular velocity oi 900 rpm clockwise dcternrinc lln39 am l mllim of the piston P when 6 I 60 Knowing that crank AB rotates about point A with i unmlam angular velocity of 900 rpm clockwise determine the l t39t li 39I at inn oi the piston P when 9 39l20o Ans 15125 1483J ms2 15126 2959J ms2 cetv 39 v u Jh A r 50111111 15121 In the two cylinder air compressor shown the connecting rods ED and BE are each 190 mm long and crank AB rotates about the xed point A with a constant angular velocity of L500 rpm clockwise Determine the acceleration of each piston when 0 0 Ans 155836J msz 336521 ms2 397 00 7 J I x quotx r I ME31 12 Mechanics of Machines Level IV Rigid body kinetics Equations of planar motion Chapter 161 to 168 G Leng 167 A 20 kg cabinet is mounted on casters that allow it to move freely u 0 on the oor It a 100 N force is applied as shown deter mine a the acceleration of the cabinet I the range of values of Ii for which the cabinet Will not tip V Ans Sins2 gt 0312m sh 1488m 168 Solve Prob 167 assuming that the casters are locked and slide on the rough oor Mk 2 025 Ans 255 ms2 gt 0 In S h S 1047 m 1619 The 75 kg rod BC connects a disk centered at A to crank CD Knowing that the disk is made to rotate at the constant speed of 180 rpm determine for the position shown the vertical compo nents of the forces exerted on rod BC by pins at B and C Ans 194 N 194J N 33 I 39 squot 7154 4 soquot 3 vquot mm L 3971 1678 A uniform slender rod of length L 900 mm and mass m 4 kg is suspended from a hinge at C A39horizontal orce P 01 magnitude 75 N is applied at end B Knowing that 71quot 225 mm detm nnno a the angular acceleration of the rod b the components 01 the reaction at C Ans a 107 K rads2 b 214 I 392 J N ME31 12 Mechanics of Machines G Leng Special Problems 1 Trigonometric equations in loop analysis Solve the equations below given that abcd are known constants a asinG b cosG c Hint Let cosd aa2 b2 sin ba2 b2 b acosG b cosd c i a sine b sincl d ii Hint Bring the terms to the RHS square each equation to eliminate the 9 terms Discussion Are there multiple solutions Why 2 Mechanisms with offset For the crankslider shown the crank length is b m and the Y coupler length is lm The crank rotates at a constant rate of a rads Write the loop equations and find the slider X l velocity and acceleration for a I I I i e I given crank orientation 9 Note that the slider is offset by a distance of e m Discussion What s the geometric constraint for the offset crank and coupler lengths How would you solve the problem if the slider slides at an angle to the X axis 3 Mechanism Synthesis The crank OP of the quick return mechanism is of length R m and rotates at a constant speed a rads Find the velocity and acceleration of the point B as the crank rotates What is the angular acceleration of the rod AB Challenge 1 Given the times for the mechanism to extend and retract how would you design the mechanism ie select R L and q This is a mechanism synthesis problem ME31 12 Mechanics of Machines G Leng 4 Force analysis Do the force analysis for the crankslider example shown in the lectures except that the mechanism now lies in the horizontal plane J quotif H o R Challenge 2 Use the linsolve function in Scilab or equivalent functions in Matlab or Mathematica to solve the equations of motion easily for different crank orientation 92 Can you automate the force analysis 5 Force balancing The figure shows the ith link of a fourbar mechanism The link is nonuniform and the mass centre is located as shown How does this change the equations of motion for the link Challenge 3 Do the force analysis of the fourbar mechanism example shown in the lectures except that the links are all nonuniform Can you adjust the mass centres of the links so that the shaking force and moment are minimized This is called force balancing Look it up in the references ME31 12 Mechanics of Machines G Leng Text F Beer E Johnston and P Cromwell quotVector Mechanics for Engineers Dynamics Ninth Edition in SI unitsquot 2010 McGraW Hill Course Website httpdynlabmpenusedusgmpelsb Level I Particle kinematics Fixed and translating frames 1 J K Chapter 11 9 to 1112 1190 The motion of a particle is defined by the equations x 2 cos wt 4151 y 1 4 cos 2771 where x and y are expressed in meters l t is expressed in seconds Show that the path of the particle 2 part of the parabola shown and determine the Velocity and the 5 neeleration when a t 0 b t 15 s glmuk J 2 I Ans a0ms 27l392 I 167t2J ms2 Mme b 2x I ms 46an ms2 3 I U 11170 5 Pin P is attached to BC and slides Freely in the slot of 0A Deter mine the rate of change 0 of the angle 0 knowing that BC moves at a constant speed 1 Express your answer in terms of it h g and 6 J Ans 0 V0h secB sin2B 0 Level II Particle kinematics Rotating reference frame i j k Chapter 1510 to 1511 15160 At the instant shown the length of the boom AB is being dgcreasg ii at the constant rate of 02 ms and the boom is being lowered a constant rate of 008 rads Determine a the velocity of poiri B b the acceleration of point B Ans a 02i 048j ms b 0038i 0032j ms2 ME3112 Mechanics of Machines 15175 15176 Knowing that at the instant shown the rod attached at B rotates with a constant counter clockwise angular velocity of 6 rads determine the angular velocity and angular acceleration of the rod attached at A Fig Pisi75 i Ans 15 krads 779 kradsz Fig P15l76 Ans 6 k rads 6235 k rads2 Level III Rigid body kinematics Chapter 151 to 159 1540 In the engine system shown thc crank AB has a constant clockni isc angular 39lcity39 of 2000 1pm For the crank position indicatcrl lt39lt i39lllllle a the angular velocity of thc connecting rod BI b tlic u39locity ol39 the piston P 39 Ans a 62K rads b 131 I ms 1 900 mm ire 15125 and 15126 Knowing that crank AB rotates about point will in Mali an angular velocity oi 900 rpm clockwise dcternrinc lln39 am l mllim of the piston P when 6 I 60 Knowing that crank AB rotates about point A with i unmlam angular velocity of 900 rpm clockwise determine the l t39t li 39I at inn oi the piston P when 9 39l20o Ans 15125 1483J ms2 15126 2959J ms2 cetv 39 v u Jh A r 50111111 15121 In the two cylinder air compressor shown the connecting rods ED and BE are each 190 mm long and crank AB rotates about the xed point A with a constant angular velocity of L500 rpm clockwise Determine the acceleration of each piston when 0 0 Ans 155836J msz 336521 ms2 397 00 7 J I x quotx r I ME31 12 Mechanics of Machines Level IV Rigid body kinetics Equations of planar motion Chapter 161 to 168 G Leng 167 A 20 kg cabinet is mounted on casters that allow it to move freely u 0 on the oor It a 100 N force is applied as shown deter mine a the acceleration of the cabinet I the range of values of Ii for which the cabinet Will not tip V Ans Sins2 gt 0312m sh 1488m 168 Solve Prob 167 assuming that the casters are locked and slide on the rough oor Mk 2 025 Ans 255 ms2 gt 0 In S h S 1047 m 1619 The 75 kg rod BC connects a disk centered at A to crank CD Knowing that the disk is made to rotate at the constant speed of 180 rpm determine for the position shown the vertical compo nents of the forces exerted on rod BC by pins at B and C Ans 194 N 194J N 33 I 39 squot 7154 4 soquot 3 vquot mm L 3971 1678 A uniform slender rod of length L 900 mm and mass m 4 kg is suspended from a hinge at C A39horizontal orce P 01 magnitude 75 N is applied at end B Knowing that 71quot 225 mm detm nnno a the angular acceleration of the rod b the components 01 the reaction at C Ans a 107 K rads2 b 214 I 392 J N ME31 12 Mechanics of Machines G Leng Special Problems 1 Trigonometric equations in loop analysis Solve the equations below given that abcd are known constants a asinG b cosG c Hint Let cosd aa2 b2 sin ba2 b2 b acosG b cosd c i a sine b sincl d ii Hint Bring the terms to the RHS square each equation to eliminate the 9 terms Discussion Are there multiple solutions Why 2 Mechanisms with offset For the crankslider shown the crank length is b m and the Y coupler length is lm The crank rotates at a constant rate of a rads Write the loop equations and find the slider X l velocity and acceleration for a I I I i e I given crank orientation 9 Note that the slider is offset by a distance of e m Discussion What s the geometric constraint for the offset crank and coupler lengths How would you solve the problem if the slider slides at an angle to the X axis 3 Mechanism Synthesis The crank OP of the quick return mechanism is of length R m and rotates at a constant speed a rads Find the velocity and acceleration of the point B as the crank rotates What is the angular acceleration of the rod AB Challenge 1 Given the times for the mechanism to extend and retract how would you design the mechanism ie select R L and q This is a mechanism synthesis problem ME31 12 Mechanics of Machines G Leng 4 Force analysis Do the force analysis for the crankslider example shown in the lectures except that the mechanism now lies in the horizontal plane J quotif H o R Challenge 2 Use the linsolve function in Scilab or equivalent functions in Matlab or Mathematica to solve the equations of motion easily for different crank orientation 92 Can you automate the force analysis 5 Force balancing The figure shows the ith link of a fourbar mechanism The link is nonuniform and the mass centre is located as shown How does this change the equations of motion for the link Challenge 3 Do the force analysis of the fourbar mechanism example shown in the lectures except that the links are all nonuniform Can you adjust the mass centres of the links so that the shaking force and moment are minimized This is called force balancing Look it up in the references

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