Large displacement analysis of elastically constrained rotating disks with rigid body degrees of freedom

2012 ◽  
Vol 54 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Ramin M.H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Large Displacement ◽  
Rotating Disks ◽  
Displacement Analysis

Force Relationships for an XYZ Micromanipulator With Three Translational Degrees of Freedom

2004 ◽  
Author(s):  
Kimberly A. Jensen ◽  
Craig P. Lusk ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Force Analysis ◽  
Displacement Analysis ◽  
Input Force ◽  
Output Force ◽  
Out Of Plane ◽  
Plane Displacement

This paper introduces the force analysis of the XYZ Micromanipulator (XYZM). The XYZM has three independent linear inputs and a positioning platform. The positioning platform remains horizontal throughout its motion and has translation in the x, y, and z directions. The design and displacement analysis for the XYZM was reported previously. This paper concentrates on the input-output force relationships and the derivation of the XYZM kinematic coefficients. Equations for the three versions of the XYZM are reported and sample results provided. Slider displacements of 45 micrometers result in a predicted out-of-plane displacement of 188 micrometers for the rigid-body XYZM and 262 micrometers for the compliant XYZM. This correlates to output force of 286 micronewtons with an input force of 150 micronewtons for the rigid-body XYZM and 261 micronewton output force with an input force of 150 micronewtons for the compliant XYZM.

On the Issue of Redundancy in the Large Rotation Vector Formulation

2014 ◽  
Author(s):  
Jieyu Ding ◽  
Michael Wallin ◽  
Cheng Wei ◽  
Antonio M. Recuero ◽  
Ahmed A. Shabana
Keyword(s):  
Rigid Body ◽  
Large Displacement ◽  
Rotation Vector ◽  
Fundamental Issue ◽  
Geometric Invariant ◽  
Large Rotation ◽  
Displacement Analysis ◽  
Space Curves ◽  
Material Points ◽  
Shed Light

In the large rotation vector formulations (LRVF), two independent interpolations are used in the nonlinear large displacement analysis of beams. This kinematic description leads to a fundamental redundancy problem. This paper examines this fundamental issue and demonstrates that the use of two geometrically independent meshes can lead to coordinate and geometric invariant redundancy that cannot be solved using constraints or forces. It is demonstrated in this paper that the two geometry meshes can define different space curves, which can differ by arbitrary rigid body displacements. The material points of the two meshes occupy different positions in the deformed configuration, and as a consequence, the geometries of the two meshes can differ significantly. Simple examples are presented in order to shed light on these fundamental issues.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Generalized Modes in Time-Domain Seakeeping Calculations

2012 ◽  
Vol 56 (04) ◽  
pp. 215-233
Author(s):  
Johan T. Tuitman ◽  
Šime Malenica ◽  
Riaan van't Veer
Keyword(s):  
Rigid Body ◽  
Transient Response ◽  
Time Domain ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Nonlinear Load ◽  
Large Amplitude Motions ◽  
Rigid Body Modes ◽  
The Time Domain

The concept of "generalized modes" is to describe all degrees of freedom by mode shapes and not using any predefined shape, like rigid body modes. Generalized modes in seakeeping computations allow one to calculate the response of a single ship, springing, whipping, multibody interaction, etc., using a uniform approach. The generalized modes have already been used for frequency-domain seakeeping calculations by various authors. This article extents the generalized modes methodology to be used for time-domain seakeeping computations, which accounts for large-amplitude motions of the rigid-body modes. The time domain can be desirable for seakeeping computations because it is easy to include nonlinear load components and to compute transient response, like slamming and whipping. Results of multibody interaction, two barges connected by a hinge, whipping response of a ferry resulting from slamming loads, and the response of a flexible barge are presented to illustrate the theory.

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