Bond Graph Modeling of Mechanical Dynamics of an Excavator for Hydraulic System Analysis and Design
This paper focuses on the development of bond graph
dynamic model of the mechanical dynamics of an excavating mechanism
previously designed to be used with small tractors, which are
fabricated in the Engineering Workshops of Jomo Kenyatta University
of Agriculture and Technology. To develop a mechanical dynamics
model of the manipulator, forward recursive equations similar to
those applied in iterative Newton-Euler method were used to obtain
kinematic relationships between the time rates of joint variables
and the generalized cartesian velocities for the centroids of the
links. Representing the obtained kinematic relationships in bondgraphic
form, while considering the link weights and momenta as
the elements led to a detailed bond graph model of the manipulator.
The bond graph method was found to reduce significantly the number
of recursive computations performed on a 3 DOF manipulator for a
mechanical dynamic model to result, hence indicating that bond graph
method is more computationally efficient than the Newton-Euler
method in developing dynamic models of 3 DOF planar manipulators.
The model was verified by comparing the joint torque expressions
of a two link planar manipulator to those obtained using Newton-
Euler and Lagrangian methods as analyzed in robotic textbooks. The
expressions were found to agree indicating that the model captures
the aspects of rigid body dynamics of the manipulator. Based on
the model developed, actuator sizing and valve sizing methodologies
were developed and used to obtain the optimal sizes of the pistons
and spool valve ports respectively. It was found that using the pump
with the sized flow rate capacity, the engine of the tractor is able to
power the excavating mechanism in digging a sandy-loom soil.
[1] J. Denavit, and R. S. Hartenberg, "A kinematic notation for lower-pair
mechanisms based on matrices," Journal of Applied Mechanics, pp. 215-
221., 1955.
[2] K.S. Fu, R. C. Gonzalez, and C. S. Lee, Robotics: Control, Sensing,
Vision and Intelligence. McGraw Hill Book Publishing Company, 1987.
[3] J. J. Craig, Introduction to Robotics: Mechanics and Control. Addison-
Wesley Publishers, USA, 1986.
[4] V. Anand, H. Kansal, and A. Singla, "Some aspects in bond graph
modeling of robotic manipulators: Angular velocities from symbolic
manipulation of rotation matrices," Technical Report, Department of
Mechanical Engineering, Sant Longowal Institute of Engineering and
Technology, 2003.
[5] H. M. Paynter, Analysis and Design of Engineering Systems. MIT Press
Publishers, Cambridge, 1961.
[6] D. C. Karnopp, D. L Margolis, and R. C. Rosenberg, System Dynamics:
Modelling and Simulation of Mechatronic Systems. John Wiley and Sons
Publishers, Newyork, 2000.
[7] D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics;
A Unified Approach. John Wiley and Sons Publishers, Newyork, 2nd ed.,
1990.
[8] D .C. Karnopp and R. C. Rosenberg, Introduction to Physical System
Dynamics. McGraw Hill Publishers, Newyork, 1983.
[9] P. Breedveld, "Bond graphs," in Encyclopedia of Life Support Systems,
Modeling and Simulation, 2003.
[10] P. Gawthrop and L. Smith, Metamodeling: Bond Graphs and Dynamic
Systems. Prentice Hall International Publishers, UK Limited, 1996.
[11] F. Fakri, A. Rocaries, and A. Carrierre, "A simple method for conversion
of bond graph models in representation by block diagrams,"
in 1997 Proc. International Conference on Bond Graph Modeling and
Simulation.
[12] J. F. Broenink, "Introduction to Physical Systems Modeling with Bond
Graphs," Technical Report, Department of Electrical Engineering, University
of Twente, Netherlands, 1996.
[13] O. M. Muvengei, "Design of an excavating mechanism to be used with
juja diesel tractor jk01," Design Innovation, Department of Mechanical
Engineering, J.K.U.A.T, 2006.
[14] A. Koivo, "Kinematics of excavator (back hoe) for transfering surface
materials," Journal of Aerospace Engineering, vol. 7(1), pp. 7-31, 1994.
[15] J. Y. Luh, M. W. Walker, and R. P. Paul, "On-line computational
scheme for mechanical manipulators," Journal of Dynamic Systems,
Measurement and Control, vol. 120, pp. 69-76, 1980.
[16] H. N. Cannon, "Extended earthmoving with an autonomous excavator,"
MSc. thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh,
1999.
[17] H. Q. Nguyen, "Robust low level control of robotic excavation". PhD.
thesis, Australian Centre for Field Robotics, The University of Sydney,
2000.
[18] S. Sarkar, "Dynamic modeling of an articulated forestry machine for
simulation and control," MSc. thesis, Department of Mechanical Engineering,
McGill University, Canada, 1996.
[19] O. M. Muvengei, "Simulation of the dynamic behavior of an excavator
due to interacting mechanical and hydraulic dynamics," MSc. thesis,
Department of Mechanical Engineering, JKUAT, Kenya, 2008.
[1] J. Denavit, and R. S. Hartenberg, "A kinematic notation for lower-pair
mechanisms based on matrices," Journal of Applied Mechanics, pp. 215-
221., 1955.
[2] K.S. Fu, R. C. Gonzalez, and C. S. Lee, Robotics: Control, Sensing,
Vision and Intelligence. McGraw Hill Book Publishing Company, 1987.
[3] J. J. Craig, Introduction to Robotics: Mechanics and Control. Addison-
Wesley Publishers, USA, 1986.
[4] V. Anand, H. Kansal, and A. Singla, "Some aspects in bond graph
modeling of robotic manipulators: Angular velocities from symbolic
manipulation of rotation matrices," Technical Report, Department of
Mechanical Engineering, Sant Longowal Institute of Engineering and
Technology, 2003.
[5] H. M. Paynter, Analysis and Design of Engineering Systems. MIT Press
Publishers, Cambridge, 1961.
[6] D. C. Karnopp, D. L Margolis, and R. C. Rosenberg, System Dynamics:
Modelling and Simulation of Mechatronic Systems. John Wiley and Sons
Publishers, Newyork, 2000.
[7] D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics;
A Unified Approach. John Wiley and Sons Publishers, Newyork, 2nd ed.,
1990.
[8] D .C. Karnopp and R. C. Rosenberg, Introduction to Physical System
Dynamics. McGraw Hill Publishers, Newyork, 1983.
[9] P. Breedveld, "Bond graphs," in Encyclopedia of Life Support Systems,
Modeling and Simulation, 2003.
[10] P. Gawthrop and L. Smith, Metamodeling: Bond Graphs and Dynamic
Systems. Prentice Hall International Publishers, UK Limited, 1996.
[11] F. Fakri, A. Rocaries, and A. Carrierre, "A simple method for conversion
of bond graph models in representation by block diagrams,"
in 1997 Proc. International Conference on Bond Graph Modeling and
Simulation.
[12] J. F. Broenink, "Introduction to Physical Systems Modeling with Bond
Graphs," Technical Report, Department of Electrical Engineering, University
of Twente, Netherlands, 1996.
[13] O. M. Muvengei, "Design of an excavating mechanism to be used with
juja diesel tractor jk01," Design Innovation, Department of Mechanical
Engineering, J.K.U.A.T, 2006.
[14] A. Koivo, "Kinematics of excavator (back hoe) for transfering surface
materials," Journal of Aerospace Engineering, vol. 7(1), pp. 7-31, 1994.
[15] J. Y. Luh, M. W. Walker, and R. P. Paul, "On-line computational
scheme for mechanical manipulators," Journal of Dynamic Systems,
Measurement and Control, vol. 120, pp. 69-76, 1980.
[16] H. N. Cannon, "Extended earthmoving with an autonomous excavator,"
MSc. thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh,
1999.
[17] H. Q. Nguyen, "Robust low level control of robotic excavation". PhD.
thesis, Australian Centre for Field Robotics, The University of Sydney,
2000.
[18] S. Sarkar, "Dynamic modeling of an articulated forestry machine for
simulation and control," MSc. thesis, Department of Mechanical Engineering,
McGill University, Canada, 1996.
[19] O. M. Muvengei, "Simulation of the dynamic behavior of an excavator
due to interacting mechanical and hydraulic dynamics," MSc. thesis,
Department of Mechanical Engineering, JKUAT, Kenya, 2008.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:57828", author = "Mutuku Muvengei and John Kihiu", title = "Bond Graph Modeling of Mechanical Dynamics of an Excavator for Hydraulic System Analysis and Design", abstract = "This paper focuses on the development of bond graph
dynamic model of the mechanical dynamics of an excavating mechanism
previously designed to be used with small tractors, which are
fabricated in the Engineering Workshops of Jomo Kenyatta University
of Agriculture and Technology. To develop a mechanical dynamics
model of the manipulator, forward recursive equations similar to
those applied in iterative Newton-Euler method were used to obtain
kinematic relationships between the time rates of joint variables
and the generalized cartesian velocities for the centroids of the
links. Representing the obtained kinematic relationships in bondgraphic
form, while considering the link weights and momenta as
the elements led to a detailed bond graph model of the manipulator.
The bond graph method was found to reduce significantly the number
of recursive computations performed on a 3 DOF manipulator for a
mechanical dynamic model to result, hence indicating that bond graph
method is more computationally efficient than the Newton-Euler
method in developing dynamic models of 3 DOF planar manipulators.
The model was verified by comparing the joint torque expressions
of a two link planar manipulator to those obtained using Newton-
Euler and Lagrangian methods as analyzed in robotic textbooks. The
expressions were found to agree indicating that the model captures
the aspects of rigid body dynamics of the manipulator. Based on
the model developed, actuator sizing and valve sizing methodologies
were developed and used to obtain the optimal sizes of the pistons
and spool valve ports respectively. It was found that using the pump
with the sized flow rate capacity, the engine of the tractor is able to
power the excavating mechanism in digging a sandy-loom soil.", keywords = "Actuators, bond graphs, inverse dynamics, recursive
equations, quintic polynomial trajectory.", volume = "3", number = "3", pages = "302-9", }