MENG 371, Chapter 8

1
MENG 372Chapter 11Dynamic Force Analysis
All figures taken from Design of Machinery, 3rd
ed. Robert Norton 2003
2
Solution using Newtons Law

• Newtons Law
• For planar motion we have

3
Center of Percussion (from Ch.10)

• The center of percussion (P) is a point on a body
  which, when struck with a force, will have
  associated with it another point called the
  center of rotation (R) at which there will be a
  zero reaction force

4
Single Link in Pure Rotation

• From free body diagram
• SFm2aFPF12
• STIgaT12
• (R12?F12)(RP?FP)
• Breaking down into components
• SFxm2axFPxF12x
• SFym2ayFPyF12y
• STIgaT12
• (R12xF12y-R12yF12x)
• (RPxFPy-RPyFPx)

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Single Link in Pure Rotation

• SFxm2axFPxF12x
• SFym2ayFPyF12y
• STIgaT12(R12xF12y-R12yF12x)
• (RPxFPy-RPyFPx)
• Putting into a matrix format

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Force Analysis of a Fourbar Linkage

• Free Body Diagrams

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Links 2 and 3

• Link 2

Link 3 (F23-F32)
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Link 4

• F34-F43

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In One Matrix Equation

• We have 9 equations and 9 unknowns

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Crank Slider

• Free Body Diagrams

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Crank Slider

• For Link 4
• 8 equations, 8 unknowns

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In One Matrix Equation

• We have 8 equations and 8 unknowns

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Inverted Crank Slider (error in the book)

• Free Body Diagrams

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Links 3 and 4
T43

• Link 3 (F23-F32)
• Link 4(F34-F43)

T34-T43
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Other equations for F43

• We know the direction of F43n

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Matrix equation with no friction

• 9 equations, 9 unknowns

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Shaking Forces and Shaking Torque

• Shaking Force sum of forces acting on the ground
  frame
• FSF21F41
• Shaking Torque (Ts) reaction torque felt by the
  ground.
• TsT21-T12

T21