ME 358 Mechanism Analysis Dr' Naghshineh

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ME 358Mechanism AnalysisDr. Naghshineh
Presented By Ryan Allen Phuong Tran
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Initial Design Requirements

• Output velocity of point on path had to be less
  than 10 in/sec.
• No guides or surfaces could be used to aid in
  motion for any parts.
• Motor had to be mounted in specified area with
  output vertical path also being in specified
  place.
• Mechanism had to fit in smallest possible box
  while allowing 6 inch clearance.

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Specified Requirements
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Final Mechanism Design
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Design Specifications

• Motor is located in center of circle which is
  located on bottom-most right of the possible
  motor mounting location.
• Circle has a 6 inch radius.
• Pivoting member connected to the circle is 42
  inches long.
• Vertical member is 20 inches long.
• Two identical horizontal members are 10 inches
  long.

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Total Area of Box

• Total area of empty box 84 inch x 34 inch
• 2856 inch2
• Area of circle p62 113.09 inch2
• Area of pivoting member 42 inch2
• Area of vertical member 20 inch2
• Area of combined horizontal members 40inch2
• Total Combined Area 2856 113.09 42 40
  3051.09 inch2

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Calculations

• Assume Slider Crank Configuration
• ?AB 0.5 rad./sec.
• aAB 1 rad./sec2
• Link 1 6 inch.
• Link 2 42 inch.
• Offset -36 inch.

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Calculation

• Case 1
• Position C is at the top of the
  vertical path.
• T 2 217 from vertical.
• T 3 arcsin((-6sin(217 )-(-36))/42)p 129.5
• D 6cos(217 )-42cos(129.5 ) 21.95inch
• This value represents the height of the position
  from the center of the circle.

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Calculation

• Velocity Analysis for case 1
• ?BC (6cos(217 ))\(42cos(129.5 )) .5 rad/sec
  .089 rad/sec.
• Vc -6(0.5)sin(217)-42(0.89)sin(129.5)
• Vc4.7j inch/sec.
• This represents a velocity moving up.

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Acceleration Calculation

• Acceleration Analysis for case 1
• aBC ( 6(1)cos(217)- 6(0.50)sin(217)
  42(0.892)sin(129.5))\(42cos(
  129.5)
• aBC0.136 rad/sec2
• Acceleration _at_ C -1sin(217)-
  6(0.52)cos(217) 420.136sin(129.5)420.89
  2cos(129.5)
• 8.99j rad/sec2

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Calculation

• Case 2
• Position C is at the center of the
  vertical path.
• T 2 41 from vertical.
• T 3 arcsin((-6sin(42)-(-36))/42)p 108.03
• D 6cos(41 )-42cos(108.03 ) 17.53inch
• This value represents the vertical distance from
  the center of the path to the center of the
  circle.

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Calculations

• Velocity Analysis for case 2
• ?BC (6cos(41))\(42cos(108.03)) .5 rad/sec
  ?BC -1.74 rad/sec.
• Vc -6(0.5)sin(41)- 42(-1.74)sin(108.03)
• Vc-8.92j inch/sec.
• This represents a velocity moving down.

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Acceleration Calculation

• Acceleration Analysis for case 2
• aBC ( 6(1)cos(41)- 6(0.50)sin(41)
  42(-1.742)sin(108.03))\(42cos(
  108.03))
• aBC-0.365 rad/sec2
• Acceleration _at_ C -1sin(41)- 6(0.52)cos(41)
  420.136sin(108.03)420.892cos(108.03)
• -20.066j rad/sec2

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Calculations

• Case 3
• Position C is at the bottom of the vertical
  path.
• T 2 59 from vertical.
• T 3 arcsin((-6sin(59)-(-36))/42)p 101.59
• D 6cos(59 )-42cos(101.59 ) 11.53inch
• This value represents the vertical distance from
  the bottom of the path to the center of the
  circle.

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Calculation

• Vertical Analysis of case 3
• ?BC (6cos(59))\(42cos(101.6)) .5 rad/sec
• ?BC -0.183 rad/sec.
• Vc -6(0.5)sin(59) - 42(-0.183)sin(101.6)
• Vc-10.02j inch/sec.
• This represents a velocity moving down.

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Acceleration Calculation

• Acceleration Analysis for case 3
• aBC ( 6(1)cos(59)- 6(0.50)sin(59)
  42(-0.1832)sin(101.59))\(42cos
  (101.59))
• aBC-0.377 rad/sec2
• Acc _at_ C -1sin(59)- 6(0.52)cos(59)
  42(-0.377)sin(101.59)42(-0.1832)cos(101.59
  )
• -21.712j rad/sec2

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Results What can we do with this?

• This mechanism design can be used for machinery
  in certain factory settings.
• May be used to lift many products, thus saving
  time, labor, and valuable floor space.
• Materials used to build this mechanism can be
  customized to make lighter or using cheaper
  materials to save money.
• Also, by adding different lengths to the arms
  the output path can be customized.

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Conclusion and Recomendations

• Easier to start design with guidelines or
  requirements that help refine rough ideas.
• Make mechanism simple compared to complex. The
  more cluttered the mechanism is with useless
  pieces it is harder to predict the behavior. Thus
  saving money and time.
• Whenever possible, contour a design mechanism
  relating to those that are familiar. Completely
  redefining and designing a mechanism puts much
  more burden on velocity and acceleration
  calculations.
• Use light materials whenever economical.
• Build a mechanism that can be easily repaired or
  maintained.

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Resources

• Design of Machinery , Third Edition. Norton,
  Robert L.
• www.howstuffworks.com
• Working Model, student edition