A Dynamic Analysis of a Spatial Mechanism With a Passive Degree of Freedom

1989 ◽  
Vol 111 (2) ◽  
pp. 238-242 ◽  
Author(s):  
C. H. Suh ◽  
H. Y. Kang
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Euler’S Equations ◽  
Kinematic Method ◽  
Euler's Equations

A method is developed for kinematic and dynamic analysis of a spatial mechanisms that has one or more links with a passive degree of freedom. The Sphere-Sphere (SS) link, the most commonly known link having a passive degree of freedom, is investigated to develop in detail displacement, velocity, and acceleration matrices for complete kinematics. The dynamic analysis of the RSSR mechanism is presented as an example, using the developed kinematic method for SS links and Euler’s equations of motion.

Complete Six-Degrees-of-Freedom Nonlinear Ship Rolling Motion

1994 ◽  
Vol 116 (4) ◽  
pp. 191-201 ◽  
Author(s):  
M. Taz Ul Mulk ◽  
J. Falzarano
Keyword(s):  
Degrees Of Freedom ◽  
Second Harmonic ◽  
Equations Of Motion ◽  
Path Following ◽  
Euler Angle ◽  
Moment Curve ◽  
Six Degrees Of Freedom ◽  
Euler’S Equations ◽  
Euler's Equations ◽  
Asymmetric Nonlinearity

The emphasis of this paper is on nonlinear ship roll motion, because roll is the most critical ship motion of all six modes of motion. However, coupling between roll and the other modes of motion may be important and substantially affect the roll. Therefore, the complete six-degrees-of-freedom Euler’s equations of motion are studied. In previous work (Falzarano et al., 1990, 1991), roll linearly coupled to sway and yaw was studied. Continuing in this direction, this work extends that analysis to consider the dynamically more exact six-degrees-of-freedom Euler’s equations of motion and associated Euler angle kinematics. A combination of numerical path-following techniques and numerical integrations are utilized to study the steady-state response determined using this more exact modeling. The hydrodynamic forces are: linear frequency-dependent added-mass, damping, and wave-exciting, which are varied on a frequency-by-frequency basis. The linearized GM approximation to the roll-restoring moment is replaced with the nonlinear roll-restoring moment curve GZ(φ), and the linear roll wave damping is supplemented by an empirically derived linear and nonlinear viscous damping. A particularly interesting aspect of this modeling is the asymmetric nonlinearity associated with the heave and pitch hydrostatics. This asymmetric nonlinearity results in distinctive “dynamic bias,” i.e., a nonzero mean in heave and pitch time histories for a zero mean periodic forcing, and a substantial second harmonic. A Fourier analysis of the nonlinear response indicates that the harmonic response is similar to the linear motion response.

Solution of Topology Embryonic Graph and Topology Graph for Unified Planar-Spatial Mechanisms

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Matrix Approach ◽  
Group Approach ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
And Topology ◽  
Topology Graph ◽  
Relative Theory

An analysis matrix approach for solving an isomeric topology embryonic graph and a digital group approach for solving an isomeric topology graph of a unified planar-spatial mechanism are presented and the relative theory is discussed. Firstly, all binary links are removed from each acceptable linkage system with different degrees of freedom, many analysis matrixes are constructed, and many topology embryonic graphs of the mechanism are derived. Secondly, from an acceptable multi-element link combination of planar or spatial mechanisms, a rule for determining the isomeric topology embryonic graphs and an unreasonable topology embryonic graph is obtained. Thirdly, by considering the degree of freedom of the mechanism and the configuration of a planar or spatial mechanism, the number of binary links is determined. Finally, all removed binary links are rearranged systematically back into an isomeric topology embryonic graph, and the acceptable topology graphs of the mechanism are derived by using a digital group approach. Some illustrations show that the two approaches are simple and effective tools and can be employed to synthesize both planar and spatial mechanisms.

scholarly journals Bumpy Spin-Down of Anomalous X-Ray Pulsars: The Link with Magnetars

2000 ◽  
Vol 177 ◽  
pp. 691-694
Author(s):  
A. Melatos
Keyword(s):  
Neutron Star ◽  
Gamma Ray ◽  
Equations Of Motion ◽  
Recurrence Time ◽  
Statistical Relation ◽  
Dipole Radiation ◽  
X Ray ◽  
Euler’S Equations ◽  
Euler's Equations

AbstractIt is argued that bumps in the timing histories Ω(t) of the anomalous X-ray pulsars (AXPs) IE 1048.1-5937 and IE 2259+586 are the signature of a magnetar undergoing radiative precession, wherein the hydromagnetic deformation of the neutron star couples to an oscillating component of the vacuum-dipole radiation torque to produce an anharmonic wobble with periodτpr∼ 10 yr. An analysis of Euler’s equations of motion for a biaxial magnet reproduces the amplitude and recurrence time of the bumps for IE 1048.1-5937 and IE 2259+586, predicts Ω(t) for the next 20 years for both objects, and predicts a testable statistical relation betweendΩ/dtandτprfor the AXP population overall. Radiative precession of soft gamma-ray repeaters is also discussed, together with implications for the internal (e.g. viscosity) and magnetospheric (e.g.e+e−pair currents) properties of magnetars.

Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements

1975 ◽  
Vol 97 (2) ◽  
pp. 739-747 ◽  
Author(s):  
Dilip Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Straight Line ◽  
Unified Method

A new, unified method is proposed and demonstrated to conduct kinematic analysis of spatial mechanisms involving revolute, cylindrical, prismatic, helical and spherical pairs. The paper derives the equations for the successive screw displacements, and the equations for pair constraints. Using these equations, closed-form relationships for displacement, velocity and acceleration of single or multi-loop spatial mechanisms are obtained by (1) breaking the mechanism at a critical joint (2) unfolding the mechanism along a straight line (3) providing successive screw displacement at each joint and (4) reassembling the mechanism to form a closed loop. The application of this newly developed approach is demonstrated by considering an example of a two-loop spatial mechanism with revolute, cylindrical and spherical pairs.

Variable Degree-of-Freedom Spatial Mechanisms Composed of Four Circular Translation Joints

2020 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Configuration Space ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Variable Degree ◽  
Circular Trajectory ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode

Abstract This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.

Composition Principle Based on Single-Open-Chain Unit for General Spatial Mechanisms and Its Application—In Conjunction With a Review of Development of Mechanism Composition Principles

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Ting-Li Yang ◽  
Anxin Liu ◽  
Huiping Shen ◽  
Lubin Hang ◽  
Qiaode Jeffery Ge
Keyword(s):  
Dynamic Analysis ◽  
General Procedure ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Kinematic Chains ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Structure Synthesis ◽  
General Method ◽  
Dimension Number

Based on the general degree-of-freedom (DOF) formula for spatial mechanisms proposed by the author in 2012, the early single open chain (SOC)-based composition principle for planar mechanisms is extended to general spatial mechanisms in this paper. First, three types of existing mechanism composition principle and their characteristics are briefly discussed. Then, the SOC-based composition principle for general spatial mechanisms is introduced. According to this composition principle, a spatial mechanism is first decomposed into Assur kinematic chains (AKCs) and an AKC is then further decomposed into a group of ordered SOCs. Kinematic (dynamic) analysis of a spatial mechanism can then be reduced to kinematic (dynamic) analysis of AKCs and finally to kinematic (dynamic) analysis of ordered SOCs. The general procedure for decomposing the mechanism into ordered SOCs and the general method for determining AKC(s) contained in the mechanism are also given. Mechanism's kinematic (dynamic) analysis can be reduced to the lowest dimension (number of unknowns) directly at the topological structure level using the SOC-based composition principle. The SOC-based composition principle provides a theoretical basis for the establishment of a unified SOC-based method for structure synthesis and kinematic (dynamic) analysis of general spatial mechanisms.

Variable degree-of-freedom spatial mechanisms composed of four circular translation joints

2021 ◽  
pp. 1-16
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Variable Degree ◽  
Circular Trajectory ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode

Abstract This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF spatial 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions and tools from algebraic geometry. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.

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