Chapter 11: Dynamic Force Analysis

Chapter 11: Dynamic Force AnalysisChapter OutcomesAt the end of this chapter, you should be able to:Calculate dynamic joint forces of mechanisms

Why Study Force Analysis?Design MechanismsDetermine if links will fail under operationPerform stress and deflection analysis on linksDetermine all loads (forces and torques) acting on linksUltimate GoalMEMB243 & MEMB331Chap. 11: Force AnalysisObjective of Force AnalysisDetermine all loads acting on the links in a mechanism to allow stress and deflection analysisDetermine input torque(s) required to produce desired motion in a mechanism (input torque = torque supplied by input device)11.0: IntroductionForward dynamics problem: Given F and m, solve for aInverse dynamics problem:Given a and m, solve for FAlso called kinetostaticsChapter 11 deals with inverse dynamics problems, as accelerations of links are assumed to be known (calculated using methods in Chapter 7)

11.1: Newtonian Solution MethodFor 2D mechanisms:

Assumption throughout this chapter: Gravitational forces (weight) are small compared to other dynamic forces acting on links produced by kinematic accelerationsWeight of links will be ignoredAssumption will be invalid when links are massive or moving slowly (have small kinematic accelerations)

Info Needed Prior to Performing Force AnalysisForce Analysis of all linksaCM of all linksMass of all linksICM of all linksExternal forces and torquesVelocity AnalysisPosition AnalysisChapter 11Chapter 7Chapter 6Chapter 4Chapter 1011.1: Newtonian Solution MethodInformation needed prior to performing force analysis:Angular acceleration of all links ()Linear acceleration of CM of all links (aCM)Mass of all linksICM of all linksAll external forces and torquesAssume all information needed are either known or already given when solving problems in this chapter11.2: Single Link in Pure RotationInfo needed:aCMmICMFPExternal load, FP is given in the diagramAssume aCM, , m and ICM are already knownMotor attached at point O2 to produce and aCM

O2PaCMFPUnknowns: Input torque and reaction force at joints

11.2: Single Link in Pure RotationO2PaCMFPRPRO2TmotorFO2

Unknowns usually input torque and reaction forces at joints:Tmotor, FO2,x, FO2,ySolve 3 equations for 3 unknowns

10Solving EquationsUsing a Matrix solver (only numeric equations):

Using Maple (both numeric and symbolic)Usually, every moving link will generate 3 equations

Sample Numerical ProblemMass of link = 0.0104 kgMoment of inertia about CM = 0.08 kgm2 = 30 = 15 rad/s2aCM = 2001 m/s2 @ 208FP = 40 N @ 0O2PaCMFP10 m5 mRO2RPSolutionUsing Matrix solver:

FO2,x = -58.4 NFO2,y = -9.77 NTmotor = 205 Nm

11.2: Single Link in Pure RotationO2PFPTmotorFO2

11.3: Threebar Crank-Slide LinkageInfo needed:2, 3aCM2, aCM3m2, m3ICM2, ICM3 FPExternal load, FP is given in the diagramAssume the rest has been obtainedMotor attached at point O2

O2ABPFPLink 2Link 3Slider crank linkageRefer to textbook: Figure 11-211.3: Threebar Crank-Slide LinkageLink 2:

Link 3:

Friction assumptionZero friction:Non-zero friction:

11.3: Threebar Crank-Slide LinkageSolve 7 equations for 7 unknowns.Solving 7 equations using a Matrix solver:

Exercise: Numerical ProblemLink 2:m2 = 0.0052 kgICM2 = 0.05 kgm22 = 602 = -10 rad/s2aCM2 = 2700 m/s2 @ -89.4Link 3:m3 = 0.0104 kgICM3 = 0.10 kgm23 = 99.593 = -136.16 rad/s2aCM3 = 3453.53 m/s2 @ 254.4Rp = 2.7 m @ 101about line ABFP: 50 N @ -45 = 0.2

11.4: Fourbar Pin Jointed LinkageExternal loads: FP acting at point P, T4 acting on Link 4Motor attached at point BUnknowns: Input torque and joint forces

O2O4PABLink 2Link 4Link 3FPT411.4: Fourbar Pin-Jointed LinkageLink 2:

Link 3:

11.4: Fourbar Pin-Jointed LinkageLink 4:

Solve 9 equations of 9 unknowns

11.5: Fourbar Slider-Crank LinkageExternal loads: FP acting at point B on sliderMotor attached at point AUnknowns: Input torque and joint forces

O2ABLink 2Link 4 (Slider)Link 3FP (acting on slider)11.5: Fourbar Slider-Crank LinkageLink 2:

Link 3:

11.5: Fourbar Slider-Crank LinkageLink 4:

Friction assumptionZero friction:Non-zero friction:Solve 9 equations for 9 unknowns

11.6: Inverted Slider-CrankNo external loadsMotor attached at point O2Unknowns: Input torque and joint forces:Tmotor, FO2,x, FO2,y, FA,x, FA,y, FB,x, FB,y, FO4,x, FO4,y3 = 4 (obtained from acceleration analysis)Assumption: No sliding friction at point B

ABO2O4Link 4Link 3Link 2311.6: Inverted Slider-CrankLink 2:

Link 3:

6Force at slider (point B) on Link 3FB has no component along axis of slip (line AB) because of no sliding friction assumptionFB only has component along axis of transmission (perpendicular to line AB)Condition to ensure 2 vectors are perpendicular, dot product of both vectors is equal to zero

B3AFB-FALink 311.6: Inverted Slider-CrankLink 4:

10 equations, but only 9 unknowns1 equation is redundantEquations 6 and 10 can be combined because they have the same 3

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11.8: Shaking Forces and Shaking Torque

Moving links deliver forces to the ground at the fixed pivots O2 and O4Set up vibrations in the structure that supports the machineFPTmotorFO4FO2O4O2-Tmotor-FO4-FO211.8: Shaking Forces and Shaking TorqueShaking force: Sum of all forces acting on the ground planeFS = -FO2 FO4Shaking torque: Reaction torque felt by the ground planeTS = -Tmotor

O4O2-Tmotor-FO4-FO211.8: Shaking Forces and Shaking Torque

Shaking force tends to move the ground support back and forthShaking torque tends to rock the ground support about the driveline axisMethods to minimize shaking force and shaking torqueBalancingAdd a flywheelShock mount framePlot of shaking force for an unbalanced crank-rocker from program FOURBARCourse OutcomesIdentify mechanisms and predict their motionCalculate the degrees of freedom of mechanismsDesign mechanisms to fulfill motion generation and quick return requirementsDetermine the positions, velocities and accelerations of links and points on mechanismsDerive SVAJ functions to fulfill cam design specificationsCalculate dynamic joint forces of mechanismsBalance simple rotating objects and pin-jointed fourbar linkagesWork in a team to analyze and modify existing mechanismsPresent completed work in oral and written formUse related computer programs to design, model and analyze mechanismsEnd of Chapter 11Thank You