MBS computer programs are increasingly becoming the main tools for the design of complex systems. Such computer programs allow for the simulation of the assembled system and they automatically account for the effect of the joint constraints and moving boundary conditions. This project provides me with the opportunity to learn how to use these programs in the important durability analysis area.

1. THE UNIVERSITY OF ILLINOIS AT CHICAGO
ME 504- Dynamics of Multi body systems.
Spring 2018
Planar Slider Crank Mechanism with a Flexible Connecting
Rod
Submitted by:
Kamal Wolly Taiwo
UIN: 656931320

2. Project Report on the simulation and Analysis of a planer slider crank Mechanism with a Flexible
Connecting Rod.
The project involves the use of both finite elements in creating the mesh for the Flexible body
connecting rod and the multibody systems (MBS) algorithms for simulation.
 Using the Finite Element Method to Create Mesh for Flexible body
 Apply reference conditions to flexible bodies in order to eliminate the mesh rigid modes
 Determine components modes in order to obtain reduced order models
 Determine the inertia shape integrals matrix expressed in the nodal form
 obtain FE file which contains flexible body data which includes data modal mass transformation
matrix, modal mass and stiffness matrices, and inertia Shape integrals in their modal form, file is
used input for the MBS software
 Prepare MBS data to be used in the analysis of mechanical joints, inertia forces, velocities of
components parts and other essential numerical data.
 Perform dynamic simulation for multi body-systems
Model Description
Planer Slider Crank Mechanism Consisting of 4 bodies
body 1 = Ground; body 2 = Crank; Body 3 = Flexible connecting rod ; Body 4 = Slider Block dimensions.
I. Dimensions
Dimensions of the slider crank mechanism
Components Cross Section Diameter (m) Length (m)
Ground 0 0
Crankshaft 6.35 x 10-3
0.1524
Connecting rod 6.35 x 10-3
0.3048
Slider block 0.01 0.1
II. Mechanical Properties
Crank Shaft and Connecting rod is Assumed to made of steel with Mechanical properties
Mass density 7.89 x 103
kg/m3
& Modulus of elasticity 2.0684 x 1011
N/m2

3. III. Joints
 Crankshaft is connected to ground with a revolute joint
 Crankshaft is connected to connecting rod by a revolute joint
 Connecting rod is connected to Slider block with a revolute joint
 Slider block is connected to ground with Prismatic Joint.
 The crank Shaft has a Simple Velocity constraints specified to constantly rotate at 124 rad/s
IV. Assumptions
 The body Coordinate Systems of each body are attached to the body mass centers
 The initial configuration of crankshaft and connecting rod are assumed to be in horizontal
position.
 The initial velocities the are velocities that correspond to the specified angular velocity of the
crank shaft.
 The slider block is assumed to have zero mass and the effect of gravity is neglected for all
bodies.
V. Defining Model of rigid body system to Software
 Body Inertia
User must define mass of each body, and moment of inertia. Where MOI= mL2
/12. The slider
block is assumed to have no mass.
 Coordinates of Origin of BCS (body coordinate system of individual bodies)
The origins are placed at the center of mass of each body and defined in the global coordinate
system.
 Initial Velocities.
The angular of the crank shaft given as 124rad/s, with its linear velocity at its center of mass
defined by the formula V=wr. The linear and Angular Velocity of the connecting rod can also be
derived similarly since they share a point of equal linear velocities (pin joint).

4.  Constraints
Constraints are selected to keep the body 1 ground fixed, define joints between bodies, and
imposing constant velocity constraint crank shaft.
Generalized Coordinate constraints
User can define the motion of the reference point, where Rx and Ry define linear motion and
theta define rotation. Imposing 3 constraints on a body by setting the values to one defines a
ground link in planer.
I. Revolute Joints
The location of the 3 revolute joints: Ground-Crank joint, Crank Shaft-Connecting joint and the
connecting rod-slider block joint) are defined by the user in the coordinate system of the two
bodies connected by each joint.
II. Prismatic joints
User needs select two points on the axis of motion of slider and define those points in the
coordinate system of the slider block and the ground.
III. Constant Velocity Constraint
Constant velocity is imposed on the crank shaft to keep the Slider crank motion continuous,
after initial velocities has been applied.
The external forces and statics constraints are set to Zero. The user can also define the
dimensions, shape and bodies for graphical purposes.

5. VI. Plots Of Rx , Ry , and Theta of Crank shaft, Connecting rod and Slider for Rigid body
 Crank
Plot of RX against time Plot of Plot of time against Ry
Plot of time against orientation parameters defined by Euler parameters.
 Connecting rod
Rx against time Ry against time

6. Orientation parameters in terms of Euler parameters theta0 and theta 3 against
Slider block
Rx against time Ry against time
VII. Model of Flexible Body
Planer beam divided into four elements and subsequently five nodes in finite element Mesh
(picture Showing Elements and Nodes)
Define the model nodes where you specify the coordinates of the node with (x, y, th) and also the
setting of this node with IK(k= x, y, th). Where setting to 1 implies it is fixed and to Zero implies the nude
is free. The floating frame of reference which defines the deformation of this flexible body is placed at
its center of mass

7. The masses of each node is also defined with node at the ends having masses of m/8 and the middle
nodes having mass m/4. The external forces acting on the model should also be defined in the global
coordinate system. In this case there are no external forces acting.
User must also input spring and Damping Coefficients if applicable in the systems. There is no spring-
damper element,
The sub models must also be defined with the user specifying the element connectivity and properties.
User should define the nodes connecting elements, element masses, cross sectional area, moment of
inertia, length, modulus of elasticity and effect of gravity on elements.
After Defining the model User runs a simulation on the preSams which acts a preprocessor and creates
an input file FE file which gives detailed information of the flexible body which can be imported to the
SigmaSams Main processor for analysis of MBS. After running simulation user can use the file created to
view the behavior of the flexible component to the modes of vibrations.

8. Shape of Modes and frequencies.
Shape of modes Frequencies, Amplification and description.
Mode 1: 137.47 Hz
Bending
Mode 2: 552.89 Hz
Bending
Mode 3: 1259.47 Hz
Bending
Mode 4: 2440.58 Hz
Bending
Mode 5: 3879.27 Hz
Bending
Mode 6: 4226.65
Axial

9. VIII. Integration of input file for flexible connecting rod from preSams into 2D slider crank
Plots of Transverse Deformation middle node against time at different modes
Mode 2 Mode 4
Mode 6
Since the deformation at mode 6 is axial, the nodes would undergo some form of axial deformation.
Axial Deformation of middle node of connecting rod at mode 6

10. Horizontal Displacement of Slider Against time for flexible connecting rod analysis.
Vertical displacement of slider against time for flexible connecting rod analysis.
Conclusion
It can be observed that the displacement of the slider remains constant when the flexible connecting
rod remains constant.

11. Appendix
PreSams input file
SAMS-Mode
2
======================================================================
=
C:Sams2000SamsDataT.dat
======================================================================
=
Analysis-Type
0
======================================================================
=
Number-of-Models
1
======================================================================
=
======================================================================
=
======================================================================
=
Model_#_1_Name
Model_#_1
======================================================================
=
Model_#_1_Parameters
1 5 1 0 1
6 0 0
======================================================================
=
Model_#_1_Nodes
1 1 1 0
-0.1524 0 0
2 0 0 0
-0.0762 0 0
3 0 0 0
0 0 0
4 0 0 0
0.0762 0 0
5 0 1 0
0.1524 0 0
======================================================================
=
Model_#_1_Nodal_Masses
0.00952 0.01904 0.01904 0.01904 0.00952
======================================================================
=
Model_#_1_Nodal_Forces
0 0 0
0 0 0

12. 0 0 0
0 0 0
0 0 0
======================================================================
=
Model_#_1_Modal_Damping
0 0 0 0 0 0
======================================================================
=
======================================================================
=
Model_#_1_Submodel_#_1
4 1
======================================================================
=
Model_#_1_Submodel_#_1_Element_Connectivity
1 0 1 2
2 0 2 3
3 0 3 4
4 0 4 5
======================================================================
=
Model_#_1_Submodel_#_1_Element_Properties
1 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
2 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
3 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
4 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
Sams input file
SAMS-Mode
2
======================================================================
=
C:Sams2000SamsDataT.dat
======================================================================
=
Analysis-Type
0
======================================================================
=
Number-of-Models
1
======================================================================
=
======================================================================
=

13. ======================================================================
=
Model_#_1_Name
Model_#_1
======================================================================
=
Model_#_1_Parameters
1 5 1 0 1
6 0 0
======================================================================
=
Model_#_1_Nodes
1 1 1 0
-0.1524 0 0
2 0 0 0
-0.0762 0 0
3 0 0 0
0 0 0
4 0 0 0
0.0762 0 0
5 0 1 0
0.1524 0 0
======================================================================
=
Model_#_1_Nodal_Masses
0.00952 0.01904 0.01904 0.01904 0.00952
======================================================================
=
Model_#_1_Nodal_Forces
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
======================================================================
=
Model_#_1_Modal_Damping
0 0 0 0 0 0
======================================================================
=
======================================================================
=
Model_#_1_Submodel_#_1
4 1
======================================================================
=
Model_#_1_Submodel_#_1_Element_Connectivity
1 0 1 2
2 0 2 3
3 0 3 4
4 0 4 5

14. ======================================================================
=
Model_#_1_Submodel_#_1_Element_Properties
1 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
2 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
3 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
4 0.0190401 3.167E-05 7.981137E-11
0.0762 206840000000 0
Presam outfile
1 15 6 3
NDPOS
-0.152400E+00 0.000000E+00 0.000000E+00-0.762000E-01 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.762000E-01 0.000000E+00
0.000000E+00
0.152400E+00 0.000000E+00 0.000000E+00
MDDIS
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
MDVEL
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
MDMAT
0.000000E+00 0.000000E+00-0.611837E-01 0.000000E+00-0.419745E-02-
0.432634E-01
0.000000E+00-0.593610E-02 0.000000E+00 0.000000E+00-0.419745E-02
0.432634E-01
0.000000E+00 0.000000E+00 0.611837E-01 0.000000E+00 0.000000E+00-
0.306990E-01
0.000000E+00-0.148957E-02 0.000000E+00 0.000000E+00 0.000000E+00
0.306990E-01
0.000000E+00 0.148957E-02 0.000000E+00 0.000000E+00 0.000000E+00-
0.306990E-01
0.000000E+00 0.000000E+00-0.206146E-01 0.000000E+00-0.476479E-03
0.145767E-01
0.000000E+00 0.673843E-03 0.000000E+00 0.000000E+00-0.476479E-03-
0.145767E-01
0.000000E+00 0.000000E+00 0.206146E-01 0.000000E+00 0.000000E+00
0.169851E-01
0.000000E+00 0.000000E+00-0.169851E-01 0.000000E+00 0.000000E+00
0.169851E-01
0.000000E+00 0.000000E+00-0.169851E-01 0.000000E+00 0.000000E+00
0.169851E-01
0.000000E+00 0.000000E+00 0.158437E-01 0.000000E+00-0.143841E-03-
0.112032E-01

15. 0.000000E+00 0.203422E-03 0.000000E+00 0.000000E+00-0.143841E-03
0.112032E-01
0.000000E+00 0.000000E+00-0.158437E-01 0.000000E+00 0.000000E+00
0.000000E+00
0.747989E-04 0.000000E+00 0.000000E+00 0.138210E-03 0.000000E+00
0.000000E+00
0.180580E-03 0.000000E+00 0.000000E+00 0.195459E-03 0.000000E+00
0.000000E+00
MDMAS
0.134045E-05 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.831637E-07 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.159684E-07 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.425259E-08 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.168320E-08
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.141791E-08
MDSTF
0.100000E+01 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.100000E+01 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.100000E+01 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.100000E+01 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.100000E+01
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.100000E+01
MDFRC
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00-0.272862E-03 0.000000E+00 0.000000E+00 0.000000E+00-
0.531435E-05
0.000000E+00 0.000000E+00 0.000000E+00-0.160431E-05 0.935472E-05
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00-
0.360308E-07
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.300012E-08
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00-
0.543608E-09

16. 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00-
0.164106E-09
0.360308E-07-0.300012E-08 0.543608E-09 0.000000E+00 0.164106E-09
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.437054E-06
0.000000E+00 0.432228E-05 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00
0.000000E+00
0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00