1 Kinematic Analysis of Kinematic Analysis of Planar Linkages Planar Linkages Chapter 4 Chapter 4 2 Vector Loop Method Vector Loop Method General method to perform kinematic analysis of General method to perform kinematic analysis of linkages, applicable from the simple to the complex linkages, applicable from the simple to the complex Determine the state of motion (position, velocity, Determine the state of motion (position, velocity, acceleration) of all other links or points of interest acceleration) of all other links or points of interest VLM VLM Attach vectors to the mechanism links to form a closed loop Attach vectors to the mechanism links to form a closed loop Choose vectors to ‘measure’ variables of interest Choose vectors to ‘measure’ variables of interest Write the vector loop equation (VLE) Write the vector loop equation (VLE) Break the vector equation into scalar components Break the vector equation into scalar components Differentiate position equations to determine velocities Differentiate position equations to determine velocities Differentiate again to determine acceleration unknowns Differentiate again to determine acceleration unknowns
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Kinematic Analysis of Planar Linkages Chapter 4 · PDF fileKinematic Analysis of Planar Linkages Chapter 4 2 ... acceleration) of all other links ... Initial guesses important for
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Kinematic Analysis of Kinematic Analysis of Planar LinkagesPlanar Linkages
Chapter 4Chapter 4
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Vector Loop MethodVector Loop Method
General method to perform kinematic analysis of General method to perform kinematic analysis of linkages, applicable from the simple to the complexlinkages, applicable from the simple to the complexDetermine the state of motion (position, velocity, Determine the state of motion (position, velocity, acceleration) of all other links or points of interestacceleration) of all other links or points of interestVLMVLM�� Attach vectors to the mechanism links to form a closed loopAttach vectors to the mechanism links to form a closed loop�� Choose vectors to ‘measure’ variables of interestChoose vectors to ‘measure’ variables of interest�� Write the vector loop equation (VLE)Write the vector loop equation (VLE)�� Break the vector equation into scalar componentsBreak the vector equation into scalar components�� Differentiate position equations to determine velocitiesDifferentiate position equations to determine velocities�� Differentiate again to determine acceleration unknownsDifferentiate again to determine acceleration unknowns
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Position AnalysisPosition Analysis
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Vector Loop MethodVector Loop Method
Do I have enough loops and good Do I have enough loops and good vectors?vectors?�� # of unknowns = # independent scalar eqns?# of unknowns = # independent scalar eqns?�� Do the variables include all those we wish to Do the variables include all those we wish to