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Truck Mounted Crane
Introduction
Many trucks are equipped with cranes for load handling. Such cranes have a number of hydraulic cylinders controlling the motion, and several mechanisms.
In this example, a rigid-body analysis of such a crane is performed in order to find cylinder forces and axle forces during an operating cycle.
Model Definition
The crane geometry, which is imported from a CAD model, is shown in Figure 1 and Figure 2. In all, it consists of 14 parts which can move relative to each other.
Figure 1: Crane geometry.
Figure 2: Close-up of link mechanisms
Table 1: Identification of the crane parts
Part
Name in model
Color in figure
Base
Base
Blue
Inner boom
Boom1
Green
Outer Boom
Boom2
Yellow
Telescopic extensions
Extension1, Extension2, Extension3
Cyan, Magenta, Gray
Boom lift cylinders
Cylinder1, Cylinder2
Red, Gray
Boom lift pistons
Piston1, Piston2
Yellow, Magenta
Inner link mechanism
Link1, Link2
Magenta, Black
Outer link mechanism
Link3, Link4
Cyan, Blue
Loads
•
Self-weight in the negative Z direction.
•
A payload of 1000 kg at the tip of the crane.
Operating cycle
The simulated working cycle consists of lifting the payload from a position far away and below the crane. The crane first moves the load upward and then inward to a position close to the crane. The trajectory of the crane tip during the operating cycle is shown in Figure 3.
Figure 3: The trajectory of the crane tip during the operating cycle.
In real life, the crane is operated by controlling three cylinder lengths:
•
The inner cylinder, which raises the inner boom.
•
The outer cylinder, which controls the angle between the inner boom and the outer boom.
•
The extension cylinders, which controls how far out the extensions are. The three cylinders are synchronized so that all of them have the same extension.
To prescribe an operating cycle, it is more convenient to use the angles of the booms as parameters instead of cylinder lengths. The parameters chosen to define the operating cycle are given in Table 2.
Table 2: Operating cycle
Position
Inner boom angle to horizontal [degrees]
Angle between Inner and outer boom [degrees]
Total extension [m]
1
-15
0
5.5
2
0
0
5.1
3
15
0
5.5
4
30
0
5.5
5
45
0
5.5
6
45
0
4.5
7
45
0
3.5
8
45
0
2.5
9
45
-30
1.5
10
45
-60
1.5
11
45
-90
1.5
12
60
-120
1.5
13
60
-135
1.5
Results and Discussion
The crane in the 9th position of the operating cycle is shown in Figure 4.
Figure 4: Crane position 9.
The forces in the cylinders controlling the boom are shown in Figure 5. Compressive forces are positive. As can be anticipated, the cylinder forces are large when the payload is far from the crane base, causing large moments around the hinges.
Figure 5: Variation of forces in boom lifting cylinders during the operating cycle.
The forces in the extension cylinders are shown in Figure 6, with a compressive force being defined as positive. When the outer boom is horizontal (position 2), no axial force is needed to maintain the position. The force is higher in the inner cylinders, since they also have to carry the weight of extension segments further out.
The forces acting on the hinge axle connecting the inner and outer booms are shown in Figure 7. In a similar way you can plot the forces acting in the connections between any parts for the crane. These results supply essential information for the structural design of such details.
Figure 6: Variation of forces in extension cylinders over the operating cycle.
Figure 7: Forces on the hinges between the main crane parts.
Notes About the COMSOL Implementation
The analysis consists of a series of stationary solutions, controlled by a sweep over the 13 parameter combinations. The parameters used are the boom angles and the total displacement of the extension cylinders.
For the boom cylinders, it is the extension of the cylinders which you can enter as input. The known parameters are the boom angles. In this model, you add extra Global Equations where the cylinder extensions are computed based on the required boom angles.
In a model like this, where there are many parts connected to each other, great care must be taken in the selection of joint types to avoid overconstraining the problem. As an example, if only Hinge joints are chosen for one of the link mechanisms, then the translation out of the plane of the crane is prescribed in closed loop. Checking the Rigid Body DOF Summary table gives useful information that helps to avoid such problems. Another possibility is to add some flexibility in the joints in overconstrained directions. This relieves the overconstraint problem.
Application Library path: Multibody_Dynamics_Module/Machinery_and_Robotics/truck_mounted_crane
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Structural Mechanics>Multibody Dynamics (mbd).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Stationary.
6
Click  Done.
Geometry 1
Import 1 (imp1)
1
In the Home toolbar, click  Import.
2
In the Settings window for Import, locate the Import section.
3
Click Browse.
4
Browse to the model’s Application Libraries folder and double-click the file truck_mounted_crane.mphbin.
5
Click Import.
Form Union (fin)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Form Union (fin).
2
In the Settings window for Form Union/Assembly, locate the Form Union/Assembly section.
3
From the Action list, choose Form an assembly.
4
Clear the Create pairs check box.
5
In the Home toolbar, click  Build All.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Structural steel.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Multibody Dynamics (mbd)
Base
1
In the Model Builder window, under Component 1 (comp1) right-click Multibody Dynamics (mbd) and choose Rigid Domain.
2
In the Settings window for Rigid Domain, type Base in the Label text field.
3
Select Domains 1, 10, 17, 22, and 23 only.
Data for Rigid Domains
1
Repeat the same operations thirteen times, entering the following data:
Label
Domain selection
Boom1
19-21
Boom2
2, 4, 13
Extension1
5, 11, 14
Extension2
6, 8, 12
Extension3
3, 7, 9
Cyliner1
29
Piston1
27
Cyliner2
30
Piston2
28
Link1
15
Link2
18, 25, 32
Link3
16
Link4
24, 26, 31
The base is kept fixed.
2
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Base.
Fixed Constraint 1
In the Physics toolbar, click  Attributes and choose Fixed Constraint.
Now define the connections between various parts of the crane.
Hinge Base-Boom1
1
In the Physics toolbar, click  Global and choose Hinge Joint.
2
In the Settings window for Hinge Joint, type Hinge Base-Boom1 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Base.
4
From the Destination list, choose Boom1.
5
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Base-Boom1 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 404 and 413 only.
Hinge Base-Cylinder1
1
In the Physics toolbar, click  Global and choose Hinge Joint.
2
In the Settings window for Hinge Joint, type Hinge Base-Cylinder1 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Base.
4
From the Destination list, choose Cylinder1.
5
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Base-Cylinder1 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 589 and 598 only.
Hinge Base-Link1
1
In the Physics toolbar, click  Global and choose Hinge Joint.
2
In the Settings window for Hinge Joint, type Hinge Base-Link1 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Base.
4
From the Destination list, choose Link1.
5
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Base-Link1 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 365 and 366 only.
Hinge Boom1-Link2
1
In the Physics toolbar, click  Global and choose Hinge Joint.
2
In the Settings window for Hinge Joint, type Hinge Boom1-Link2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom1.
4
From the Destination list, choose Link2.
5
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Boom1-Link2 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 414 and 423 only.
Slot Link1-Link2
1
In the Physics toolbar, click  Global and choose Slot Joint.
2
In the Settings window for Slot Joint, type Slot Link1-Link2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Link1.
4
From the Destination list, choose Link2.
5
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Slot Link1-Link2 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 362 and 363 only.
Slot Link1-Piston1
1
In the Model Builder window, right-click Slot Link1-Link2 and choose Duplicate.
2
In the Settings window for Slot Joint, type Slot Link1-Piston1 in the Label text field.
3
Locate the Attachment Selection section. From the Destination list, choose Piston1.
Prismatic Cylinder1-Piston1
1
In the Physics toolbar, click  Global and choose Prismatic Joint.
2
In the Settings window for Prismatic Joint, type Prismatic Cylinder1-Piston1 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Cylinder1.
4
From the Destination list, choose Piston1.
5
Locate the Axis of Joint section. From the list, choose Select a parallel edge.
6
Select the Reverse direction check box.
7
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Prismatic Cylinder1-Piston1 node, then click Center of Joint: Boundary 1.
2
Select Boundary 710 only.
Joint Axis 1
1
In the Model Builder window, click Joint Axis 1.
2
Select Edge 1564 only.
Hinge Base-Boom1, Hinge Base-Cylinder1, Hinge Base-Link1, Hinge Boom1-Link2, Prismatic Cylinder1-Piston1, Slot Link1-Link2, Slot Link1-Piston1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd), Ctrl-click to select Hinge Base-Boom1, Hinge Base-Cylinder1, Hinge Base-Link1, Hinge Boom1-Link2, Slot Link1-Link2, Slot Link1-Piston1, and Prismatic Cylinder1-Piston1.
Hinge Boom1-Boom2
1
Right-click and choose Duplicate.
2
In the Settings window for Hinge Joint, type Hinge Boom1-Boom2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom1.
4
From the Destination list, choose Boom2.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Boom1-Boom2 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 438 and 439 only.
Hinge Boom1-Cylinder2
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Hinge Base-Cylinder1.1.
2
In the Settings window for Hinge Joint, type Hinge Boom1-Cylinder2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom1.
4
From the Destination list, choose Cylinder2.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Boom1-Cylinder2 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 424 and 433 only.
Hinge Boom1-Link3
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Hinge Base-Link1.1.
2
In the Settings window for Hinge Joint, type Hinge Boom1-Link3 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom1.
4
From the Destination list, choose Link3.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Boom1-Link3 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 391 and 392 only.
Hinge Boom2-Link4
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Hinge Boom1-Link2.1.
2
In the Settings window for Hinge Joint, type Hinge Boom2-Link4 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom2.
4
From the Destination list, choose Link4.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Hinge Boom2-Link4 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 603 and 604 only.
Slot Link3-Link4
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Slot Link1-Link2.1.
2
In the Settings window for Slot Joint, type Slot Link3-Link4 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Link3.
4
From the Destination list, choose Link4.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Slot Link3-Link4 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 388 and 389 only.
Slot Link3-Piston2
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Slot Link1-Piston1.1.
2
In the Settings window for Slot Joint, type Slot Link3-Piston2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Link3.
4
From the Destination list, choose Piston2.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Slot Link3-Piston2 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 388 and 389 only.
Prismatic Cylinder2-Piston2
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd) click Prismatic Cylinder1-Piston1.1.
2
In the Settings window for Prismatic Joint, type Prismatic Cylinder2-Piston2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Cylinder2.
4
From the Destination list, choose Piston2.
5
Locate the Axis of Joint section. Clear the Reverse direction check box.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Prismatic Cylinder2-Piston2 node, then click Center of Joint: Boundary 1.
2
In the Settings window for Center of Joint: Boundary, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundary 746 only.
Joint Axis 1
1
In the Model Builder window, click Joint Axis 1.
2
In the Settings window for Joint Axis, locate the Edge Selection section.
3
Click  Clear Selection.
4
Select Edge 1682 only.
Prismatic Boom2-Extension1
1
In the Physics toolbar, click  Global and choose Prismatic Joint.
2
In the Settings window for Prismatic Joint, type Prismatic Boom2-Extension1 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Boom2.
4
From the Destination list, choose Extension1.
5
Locate the Axis of Joint section. Specify the e0 vector as
0
x
1
y
0
z
6
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Prismatic Boom2-Extension1 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 315 and 316 only.
Prismatic Extension1-Extension2
1
In the Physics toolbar, click  Global and choose Prismatic Joint.
2
In the Settings window for Prismatic Joint, type Prismatic Extension1-Extension2 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Extension1.
4
From the Destination list, choose Extension2.
5
Locate the Axis of Joint section. Specify the e0 vector as
0
x
1
y
0
z
6
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Prismatic Extension1-Extension2 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 280 and 284 only.
Prismatic Extension2-Extension3
1
In the Physics toolbar, click  Global and choose Prismatic Joint.
2
In the Settings window for Prismatic Joint, type Prismatic Extension2-Extension3 in the Label text field.
3
Locate the Attachment Selection section. From the Source list, choose Extension2.
4
From the Destination list, choose Extension3.
5
Locate the Axis of Joint section. Specify the e0 vector as
0
x
1
y
0
z
6
Locate the Joint Forces and Moments section. From the list, choose Computed using weak constraints.
Center of Joint: Boundary 1
1
In the Model Builder window, expand the Prismatic Extension2-Extension3 node, then click Center of Joint: Boundary 1.
2
Select Boundaries 223 and 224 only.
Check that there are now five remaining degrees of freedom, one for each cylinder.
3
In the Model Builder window, click Multibody Dynamics (mbd).
4
In the Settings window for Multibody Dynamics, click to expand the Rigid Body DOF Summary section.
Gravity 1
1
In the Physics toolbar, click  Domains and choose Gravity.
2
In the Settings window for Gravity, locate the Domain Selection section.
3
From the Selection list, choose All domains.
Body Load 1
1
In the Physics toolbar, click  Domains and choose Body Load.
2
Select Domain 3 only.
3
In the Settings window for Body Load, locate the Force section.
4
From the Load type list, choose Total force.
5
Specify the Ftot vector as
0
x
0
y
-1000[kg]*g_const
z
Now, prescribe the position of all cylinders. The operation of three extension cylinders is synchronized.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
Angle1
0[deg]
0 rad
Angle to horizontal, inner boom
RelAng
0[deg]
0 rad
Angle between booms
ExtLen
0[m]
0 m
Total extension length
Multibody Dynamics (mbd)
1
Click the  Show More Options button in the Model Builder toolbar.
2
In the Show More Options dialog box, in the tree, select the check box for the node Physics>Equation-Based Contributions.
3
Click OK.
Global Equations 1
1
In the Physics toolbar, click  Global and choose Global Equations.
2
In the Settings window for Global Equations, locate the Global Equations section.
3
In the table, enter the following settings:
Name
f(u,ut,utt,t) (1)
Initial value (u_0) (1)
Initial value (u_t0) (1/s)
Description
cyl1Pos
Angle1-mbd.hgj1.th*180/pi
0
0
Inner cylinder extension
4
Locate the Units section. Click  Select Dependent Variable Quantity.
5
In the Physical Quantity dialog box, type displacement in the text field.
6
Click  Filter.
7
In the tree, select General>Displacement (m).
8
Click OK.
9
In the Settings window for Global Equations, locate the Global Equations section.
10
In the table, enter the following settings:
Name
f(u,ut,utt,t) (1)
Initial value (u_0) (m)
Initial value (u_t0) (m/s)
Description
cyl2Pos
RelAng-mbd.hgj5.th*180/pi
0
0
Outer cylinder extension
Prismatic Cylinder1-Piston1
In the Model Builder window, click Prismatic Cylinder1-Piston1.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Translational Motion section.
3
In the up text field, type cyl1Pos.
The prescribed displacements for the boom cylinders are given by the global equations. They must not couple back into the equation system through reaction forces.
4
Click to expand the Reaction Force Settings section. Select the Apply reaction only on joint variables check box.
Prismatic Cylinder2-Piston2
In the Model Builder window, click Prismatic Cylinder2-Piston2.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Translational Motion section.
3
In the up text field, type cyl2Pos.
4
Locate the Reaction Force Settings section. Select the Apply reaction only on joint variables check box.
Prismatic Boom2-Extension1
In the Model Builder window, click Prismatic Boom2-Extension1.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Translational Motion section.
3
In the up text field, type ExtLen/3.
Prismatic Extension1-Extension2
In the Model Builder window, click Prismatic Extension1-Extension2.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Translational Motion section.
3
In the up text field, type ExtLen/3.
Prismatic Extension2-Extension3
In the Model Builder window, click Prismatic Extension2-Extension3.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Translational Motion section.
3
In the up text field, type ExtLen/3.
Since this is a rigid body analysis, the only requirement on the mesh is that it can resolve the geometry. Apart from that, it should be as coarse as possible in order to minimize storage and computations.
Mesh 1
Free Tetrahedral 1
1
In the Model Builder window, expand the Mesh 1 node.
2
Right-click Component 1 (comp1)>Mesh 1 and choose Free Tetrahedral.
Size
1
In the Settings window for Size, locate the Element Size section.
2
From the Predefined list, choose Finer.
Size 1
1
In the Model Builder window, expand the Component 1 (comp1)>Mesh 1>Free Tetrahedral 1 node.
2
Right-click Free Tetrahedral 1 and choose Size.
3
In the Settings window for Size, locate the Geometric Entity Selection section.
4
From the Geometric entity level list, choose Domain.
5
Select Domains 2–4, 10, 15–24, 31, and 32 only.
Size 2
1
In the Model Builder window, right-click Free Tetrahedral 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Fine.
4
Locate the Geometric Entity Selection section. From the Geometric entity level list, choose Domain.
5
Select Domains 5–7, 17–20, 23, and 24 only.
6
In the Model Builder window, right-click Mesh 1 and choose Build All.
Study 1
Step 1: Stationary
1
In the Model Builder window, under Study 1 click Step 1: Stationary.
2
In the Settings window for Stationary, click to expand the Study Extensions section.
3
Select the Auxiliary sweep check box.
The positions for the operating cycle are stored on file.
4
Click  Load from File.
5
Browse to the model’s Application Libraries folder and double-click the file truck_mounted_crane_solparam.txt.
6
From the Run continuation for list, choose No parameter.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Dependent Variables 1 node, then click comp1.ODE1.
4
In the Settings window for State, locate the Scaling section.
5
From the Method list, choose Manual.
6
In the Scale text field, type 0.1.
7
In the Model Builder window, click Stationary Solver 1.
8
In the Settings window for Stationary Solver, locate the General section.
9
In the Relative tolerance text field, type 1e-6.
Step 1: Stationary
1
In the Model Builder window, click Step 1: Stationary.
2
In the Settings window for Stationary, click to expand the Results While Solving section.
3
Select the Plot check box.
4
In the Study toolbar, click  Compute.
Results
Displacement (mbd)
1
In the Settings window for 3D Plot Group, locate the Data section.
2
From the Parameter value (Angle1 (rad),RelAng (rad),ExtLen (m)) list, choose 9: Angle1=45 rad, RelAng=-30 rad, ExtLen=1.5 m.
3
In the Displacement (mbd) toolbar, click  Plot.
4
Click the  Zoom Extents button in the Graphics toolbar.
Boom cylinder forces
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Boom cylinder forces in the Label text field.
Global 1
1
Right-click Boom cylinder forces and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
mbd.prj1.Fl1
kN
Cylinder 1
mbd.prj2.Fl1
kN
Cylinder 2
4
Click to expand the Coloring and Style section. In the Width text field, type 2.
5
Find the Line markers subsection. From the Marker list, choose Cycle.
6
From the Positioning list, choose In data points.
Boom cylinder forces
1
In the Model Builder window, click Boom cylinder forces.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Force [kN].
5
Click to expand the Title section. From the Title type list, choose None.
6
In the Boom cylinder forces toolbar, click  Plot.
Extension cylinder forces
1
Right-click Boom cylinder forces and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Extension cylinder forces in the Label text field.
Global 1
1
In the Model Builder window, expand the Boom cylinder forces 1 node, then click Results>Extension cylinder forces>Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
mbd.prj3.Fl1
kN
Extension cylinder 1
mbd.prj4.Fl1
kN
Extension cylinder 2
mbd.prj5.Fl1
kN
Extension cylinder 3
4
In the Extension cylinder forces toolbar, click  Plot.
Hinge forces
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Hinge forces in the Label text field.
Global 1
1
Right-click Hinge forces and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
mbd.hgj1.Fy
kN
Inner hinge force, y
mbd.hgj1.Fz
kN
Inner hinge force, z
mbd.hgj5.Fy
kN
Outer hinge force, y
mbd.hgj5.Fz
kN
Outer hinge force, z
4
Locate the Coloring and Style section. In the Width text field, type 2.
5
Find the Line markers subsection. From the Marker list, choose Cycle.
6
From the Positioning list, choose In data points.
Hinge forces
1
In the Model Builder window, click Hinge forces.
2
In the Settings window for 1D Plot Group, locate the Legend section.
3
From the Position list, choose Lower right.
4
Locate the Plot Settings section. Select the y-axis label check box.
5
In the associated text field, type Force [kN].
6
Locate the Title section. From the Title type list, choose None.
7
In the Hinge forces toolbar, click  Plot.
Crane tip trajectory
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Crane tip trajectory in the Label text field.
Point Graph 1
1
Right-click Crane tip trajectory and choose Point Graph.
2
Select Point 350 only.
3
In the Settings window for Point Graph, locate the y-Axis Data section.
4
In the Expression text field, type w.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type v.
7
Click to expand the Coloring and Style section. In the Width text field, type 2.
8
Find the Line markers subsection. From the Marker list, choose Circle.
9
From the Positioning list, choose In data points.
Crane tip trajectory
1
In the Model Builder window, click Crane tip trajectory.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
Locate the Axis section. Select the Preserve aspect ratio check box.
5
In the Crane tip trajectory toolbar, click  Plot.