Rigid-Body Parameters for Molecular Docking Applications

2014 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Molecular Docking ◽  
Rigid Body ◽  
Body Position ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Robot Hand ◽  
Position And Orientation ◽  
Body Parameters ◽  
And Robotics

In mechanisms and robotics it is common to describe motions relative to a ground link, or robot base, and the position and orientation of the distal link (or robot hand) is viewed as a rigid-body motion relative to this fixed world frame. Assessing preferred relative rigid-body position and orientation in interacting biomolecules (such as proteins) often uses this approach as well by artificially calling one molecule the ground, and considering the motions of another molecule relative to it. But since both molecules are floating, it is not as natural to take this perspective as it is in the field of mechanisms and robotics. Therefore, this paper introduces a ‘symmetrical’ parameterization of relative biomolecular motions in which the structure of the equations is the same when each molecule views the other. In this way, there is no bias in terms of labeling one molecule as being fixed and the other as moving. The properties of this new parameterization are evaluated and compared with traditional ones known to the kinematics community.

Comparison of Methods for Determining Screw Parameters of Finite Rigid Body Motion From Initial and Final Position Data

1989 ◽  
Author(s):  
R. G. Fenton ◽  
X. Shi
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Final Position ◽  
Comparison Of Methods ◽  
Rodrigues Formula ◽  
Position Data ◽  
Data Error

Abstract Five methods for determining the screw parameters of finite rigid body motion using position data of three non-collinear points are compared on the basis of their efficiency, accuracy, and sensitivity to data error. It is found that the method based on Rodrigues’ Formula (Bottema & Roth’s method) is the most efficient. Angeles’ method and Laub & Shiflett’s method provide approximately the same level of accuracy, which is superior to that of the other methods. In terms of sensitivity, Bottema & Roth’s method is preferable On the basis of this study it is recommended that Bottema & Roth’s method to be used if uncertainty exists in the data since it can provide a solution efficiently, accurately, and it is the least sensitive to data error.

Comparison of Methods for Determining Screw Parameters of Finite Rigid Body Motion From Initial and Final Position Data

1990 ◽  
Vol 112 (4) ◽  
pp. 472-479 ◽  
Author(s):  
R. G. Fenton ◽  
Xiaolun Shi
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
The Other ◽  
Body Motion ◽  
Final Position ◽  
Comparison Of Methods ◽  
Rodrigues Formula ◽  
Position Data ◽  
Data Error

Five methods for determining screw parameters of finite rigid body motion, using position data of three noncollinear points, are compared on the basis of their efficiency, accuracy, and sensitivity to data error. It is found that the method based on Rodrigues’ Formula (Bottema and Roth’s method) is the most efficient. Angeles’ method and Laub and Shiflett’s method provide approximately the same level of accuracy, which is superior to that of the other methods. In terms of sensitivity, Bottema and Roth’s method is preferable. On the basis of this study it is recommended that Bottema and Roth’s method be used if uncertainty exists in the data, since it can provide a solution efficiently, accurately and it is the least sensitive to data error.

Convolution Metrics for Rigid Body Motion

1998 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Path Generation ◽  
Rigid Body Motions ◽  
And Robotics

Abstract Recently, the importance of metrics on the group of rigid body motions has been addressed in a number of works in the kinematics and robotics literature. This paper defines a new kind of metric on motion which is particularly easy to compute. It is shown how this metric is applicable to path generation for rigid body motions.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

Structures of the Phosphazenes [ClC(NPCl3)2]+PCl6 − and [CH3C(NPCl3)2]+SbCl6 − at 90 K

1997 ◽  
Vol 53 (6) ◽  
pp. 953-960 ◽  
Author(s):  
F. Belaj
Keyword(s):  
Rigid Body ◽  
Motion Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Torsion Angles ◽  
Ionic Compounds ◽  
Intramolecular Motions

The asymmetric units of both ionic compounds [N-(chloroformimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachlorophosphate, [ClC(NPCl3)2]+PCl^{-}_{6} (1), and [N-(acetimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachloroantimonate, [CH3C(NPCl3)2]+SbCl^{-}_{6} (2), contain two formula units with the atoms located on general positions. All the cations show cis–trans conformations with respect to their X—C—N—P torsion angles [X = Cl for (1), C for (2)], but quite different conformations with respect to their C—N—P—Cl torsion angles. Therefore, the two NPCl3 groups of a cation are inequivalent, even though they are equivalent in solution. The very flexible C—N—P angles ranging from 120.6 (3) to 140.9 (3)° can be attributed to the intramolecular Cl...Cl and Cl...N contacts. A widening of the C—N—P angles correlates with a shortening of the P—N distances. The rigid-body motion analysis shows that the non-rigid intramolecular motions in the cations cannot be explained by allowance for intramolecular torsion of the three rigid subunits about specific bonds.

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