Project

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Project

• Analysis of Amusement Park Ride

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6
8
4
7
1
6,7
5
2
5
8
3
4
1
0
0
4
2,3
9 bodies, 8 revolute joints, 1 prismatic joint M
6(9-1) 5(9) 3
5
axes of Hooke joint are perpendicular
180
6
8
4
7
6
1
6,7
3
5
2
5
8
4
1
0
4
2,3
0
7
8
4
7
6
1
6,7
3
5
2
5
8
4
1
0
4
2,3
0
8
a7
a6
a2
8
a5
4
7
6
1
6,7
3
5
2
a4
a3
5
8
4
ZF
a8
1
0
4
XF
2,3
a1
0
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Distance along ZF axis between origin of fixed
coordinate system and origin of link 8 coordinate
system is 654 2(9) 636 inches.
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Z8
6,7
7S8
5
8
X8
4
ZF
a8
1
0
4
XF
2,3
0
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Problem Statement

• given
• constant mechanism parameters
• angle f1 and f8 (angle from a8 to xF about 8S0)
• angular velocities
• angular accelerations
• location of rider (point A) in 4th coordinate
  system
• find
• position of point A measured in fixed coordinate
  system
• linear velocity and linear acceleration of point
  A measured in fixed coordinate system

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Procedure

• do position analysis
• do velocity analysis
• do acceleration analysis

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Position Analysis

• To resolve the extra degree of freedom, choose
  0f1 1?2 180?. This will keep a2 pointed
  opposite to xF.
• Determine the location of the center of the ball
  and socket joints as measured in the fixed
  coordinate system. This will give F(4S5) and
  the distance 4S5.
• Get . The second column represents Fy4,
  which is along F(4S5) and thus known.

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• The cosine of 3?4 is determined from the 2,2
  element of the array. Select the appropriate
  value for 3?4, i.e.0 ? 3?4 ? ?.
• The corresponding sine and cosine of 2?3 are
  determined from the 1,2 and 3,2 elements.

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Position Analysis

• Get going the other way around the
  chain.

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Position Analysis

• Get going the regular way around the
  chain.

All these terms are now known in terms of given
and calculated parameters.
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Position Analysis

• The angle 6?7 is obtained from the 3,2 element
  of the array. (choose one of the inverse cosine
  values)
• The corresponding value for the angle 5?6 can be
  determined from the 3,1 and 3,3 elements of
  the arrays.
• The angle (7?8 0f8) is determined from the
  1,2 and 2,2 elements of the arrays.

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Velocity Analysis

• solve 6 scalar equations in 6 unknowns
• get
• get

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Acceleration Analysis
revolute joint
prismatic joint
Note Body 9 is body 0.
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Acceleration Analysis
revolute joint
prismatic joint
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Acceleration Analysis

• solve 6 scalar equations in 6 unknowns
• get
• get