Wittenburg's formulation of multibody dynamics equations from a graph-theoretic perspective

McPhee, John; Ishac, Milad G.; Andrews, Gordon C.

doi:10.1016/0094-114x(95)00064-6

Cited by 20 publications

(14 citation statements)

References 6 publications

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“…Grimm and Waldschmidt (1997) describe a graph-based model to describe mixed signal systems. Linear graph techniques have been used to model rigid body dynamics (McPhee et al, 1996). More recently, Diaz-Calderon et al (1999) have extended this linear graph theory to include n-terminal elements and software components.…”

Section: Related Workmentioning

confidence: 99%

Kinematics Support for Design and Simulation of Mechatronic Systems

Sinha

Paredis

Khosla

2002

From Knowledge Intensive CAD to Knowledge Intensive Engineering

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Abstract:We present a framework that verifies and maintains the consistency between the representations of the form, function and behavior of mechatronic devices. These three aspects of the device represent the geometry, the task, and the actions taken to realize the task, respectively (Pahl and Beitz, 1996). They evolve simultaneously through the design process. When the designer makes a change to one aspect of the representation, our framework automatically updates all other aspects impacted by this change and reports inconsistencies. Inconsistencies occur when the kinematic behavior of the device does not match the form, or the kinematic behavior does not match the currently specified functional description. Continuous feedback of this nature shortens the design-simulate cycle for product design. To represent the components in the device we use a port-based modeling paradigm. Components encapsulate both form and behavior and are interconnected to form the system model of the device. Simulation models for the components are defined in VHDL-AMS and are solved with a commercial solver.

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Section: Related Workmentioning

confidence: 99%

Kinematics Support for Design and Simulation of Mechatronic Systems

Sinha

Paredis

Khosla

2002

From Knowledge Intensive CAD to Knowledge Intensive Engineering

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“…As suggested in the abovementioned paper [103], when the system consists in closed loop mechanisms, the concept of fundamental circuits is helpful in finding a set of closed-loop equations which constrain the system dynamics, while the concept of fundamental cutset can be applied to the vector-network diagram, to represent, essentially, the moment or force that would be obtained from a freebody diagram. The fundamental cut-set is needed, in particular, in order to select, from the whole set of inertial and external forces and torques, those which affect each single body.…”

Section: Dynamic Analysis and Simulation Of Multi-body Systemsmentioning

confidence: 99%

“…It should be acknowledged that the use of graphs to represent system topology during the generation of the governing equations of motion in multi-body dynamic systems has been exploited by Andrews and his coworkers [97][98][99][100], Sheth and Uicker [101] and by Wittenburg [102,103]. In Wittenburg's graph rigid bodies represent not only graph vertices and the edges of the kinematic pairs, but also spring-damper elements.…”

Section: Dynamic Analysis and Simulation Of Multi-body Systemsmentioning

confidence: 99%

“…Later, in 1996, McPhee et al noticed [103] that this method was not easy to be fully automated and therefore pointed out a different approach called vector-network technique, according to which the equations governing the motion of a large class of mechanisms, namely, the tree-structured systems, could be obtained by writing the cutset equations for an augmented form of Wittenburg's graph that contains mass and force elements. In order to explain better this concept, some more properties and definitions will be herein added, to those already introduced in Sections3.2.6 and 5:…”

Section: Dynamic Analysis and Simulation Of Multi-body Systemsmentioning

confidence: 99%

See 1 more Smart Citation

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

Pennestrı̀

Belfiore

2015

Mechanism and Machine Theory

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This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms. Although such idea gave its main outcome in Type and Number Synthesis (which has been much better and extensively described in another paper of the present special issue) some other intriguing side effects appeared, later in Mechanism Science, which yielded several results, and are still in the center of research and industrial world interest, such as, to name but a few, the automatic generation of the equations governing kinematic, static force and dynamic analysis of mechanisms and geared trains, the power flow analysis, the computation of the efficiency and, finally, the never fully explored structure-to-function mapping, which the present contribution points out to be still a challenge in the field

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“…Roe 26 and Koenig 13 apply the theory of linear graphs to the systems theory and provide important results that can be directly related to the two basic laws in circuit theory: Kirchhoff's voltage and current laws. Linear graph theory has been used in the analysis of rigid body dynamics 14,17,18,19,30 and in the analysis of other engineering systems that include interaction between different energy domains 21 .…”

Section: Introductionmentioning

confidence: 99%