Adding kinematic constraints to purely differential dynamics

Masarati, Pierangelo

doi:10.1007/s00466-010-0539-4

Cited by 8 publications

(4 citation statements)

References 32 publications

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“…Using a traditional Lagrange formulation to constrain closed-loop mechanisms in the presence of initial-value singularities is a problem, because the introduction of any non-zero initial value in state variables produces a permanent error in position constraints. To reduce this error and to deal with singularities simultaneously, we use Baumgarte's method [14] further developed by Masarati [15]. Using constraint equations with Baumgarte's method eliminates invalid initial value guesses over successive simulation steps, with the α and β terms (introduced in [14]) behaving like a second order system to minimize error over successive integrations.…”

Section: Integration and Solvingmentioning

confidence: 99%

An Integrated Design and Simulation Environment for Rapid Prototyping of Laminate Robotic Mechanisms

Sharifzadeh

Khodambashi

Aukes

2018

Volume 5B: 42nd Mechanisms and Robotics Conference

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Laminate mechanisms are a reliable concept in producing lowcost robots for educational and commercial purposes. These mechanisms are produced using low-cost manufacturing techniques which have improved significantly during recent years and are more accessible to novices and hobbyists. However, iterating through the design space to come up with the best design for a robot is still a time consuming and rather expensive task and therefore, there is still a need for model-based analysis before manufacturing. Until now, there has been no integrated design and analysis software for laminate robots. This paper addresses some of the issues surrounding laminate analysis by introducing a companion to an existing laminate design tool that automates the generation of dynamic equations and produces simulation results via rendered plots and videos. We have validated the accuracy of the software by comparing the position, velocity and acceleration of the simulated mechanisms with the measurements taken from physical laminate prototypes using a motion capture system.

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Section: Integration and Solvingmentioning

confidence: 99%

An Integrated Design and Simulation Environment for Rapid Prototyping of Laminate Robotic Mechanisms

Sharifzadeh

Khodambashi

Aukes

2018

Volume 5B: 42nd Mechanisms and Robotics Conference

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“…Alternatively, eliminating the constraints delivers a UCS approach. UCS methods can also be obtained through penalty formulations [4] or with the force projection approach in [24].…”

Section: Coordinates Selectionmentioning

confidence: 99%

Assessment of Linearization Approaches for Multibody Dynamics Formulations

González

Masarati

Cuadrado

et al. 2017

Journal of Computational and Nonlinear Dynamics

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Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples

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“…The problem is analyzed using a two-node variant of the previously mentioned finite volume beam formulation, also implemented in MBDyn, which was recently presented in Masarati. 38 Ten two-node beam elements are used for each beam.…”

Section: Lateral-torsional Buckling Of Right-angle Framementioning

confidence: 99%

Robust static analysis using general-purpose multibody dynamics

Masarati

2014

Proceedings of the Institution of Mechanical Engineers, Part K:

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This work discusses the implementation of a pseudo-arc-length algorithm in general-purpose multibody formulations. Such algorithm and implementation support the analysis of static problems subjected to bifurcations and turning points, expanding the applicability of such formulations. Its application to existing free general-purpose simulation software made the analysis of nontrivial static structural problems possible. Several examples of applications are presented and compared with existing solutions obtained from state-of-the-art formulations.

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Adding kinematic constraints to purely differential dynamics

Cited by 8 publications

References 32 publications

An Integrated Design and Simulation Environment for Rapid Prototyping of Laminate Robotic Mechanisms

An Integrated Design and Simulation Environment for Rapid Prototyping of Laminate Robotic Mechanisms

Assessment of Linearization Approaches for Multibody Dynamics Formulations

Robust static analysis using general-purpose multibody dynamics

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