scholarly journals A coordinate-system-independent method for comparing joint rotational mobilities

2020 ◽  
Vol 223 (18) ◽  
pp. jeb227108
Author(s):  
Armita R. Manafzadeh ◽  
Stephen M. Gatesy
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Rotational Mobility ◽  
Coordinate Systems ◽  
Map Projection ◽  
Fold Reduction ◽  
Euler Space ◽  
Rotational Degrees Of Freedom ◽  
Alternative Spaces

ABSTRACTThree-dimensional studies of range of motion currently plot joint poses in a ‘Euler space’ whose axes are angles measured in the joint's three rotational degrees of freedom. Researchers then compute the volume of a pose cloud to measure rotational mobility. However, pairs of poses that are equally different from one another in orientation are not always plotted equally far apart in Euler space. This distortion causes a single joint's mobility to change when measured based on different joint coordinate systems and precludes fair comparison among joints. Here, we present two alternative spaces inspired by a 16th century map projection – cosine-corrected and sine-corrected Euler spaces – that allow coordinate-system-independent comparison of joint rotational mobility. When tested with data from a bird hip joint, cosine-corrected Euler space demonstrated a 10-fold reduction in variation among mobilities measured from three joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function.

Interstitial Nucleus of Cajal Encodes Three-Dimensional Head Orientations in Fick-Like Coordinates

2007 ◽  
Vol 97 (1) ◽  
pp. 604-617 ◽  
Author(s):  
Eliana M. Klier ◽  
Hongying Wang ◽  
J. Douglas Crawford
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Semicircular Canals ◽  
Head Rotation ◽  
Head Orientation ◽  
Interstitial Nucleus Of Cajal ◽  
The Gaze ◽  
Behavioral Constraints ◽  
The Right

Two central, related questions in motor control are 1) how the brain represents movement directions of various effectors like the eyes and head and 2) how it constrains their redundant degrees of freedom. The interstitial nucleus of Cajal (INC) integrates velocity commands from the gaze control system into position signals for three-dimensional eye and head posture. It has been shown that the right INC encodes clockwise (CW)-up and CW-down eye and head components, whereas the left INC encodes counterclockwise (CCW)-up and CCW-down components, similar to the sensitivity directions of the vertical semicircular canals. For the eyes, these canal-like coordinates align with Listing’s plane (a behavioral strategy limiting torsion about the gaze axis). By analogy, we predicted that the INC also encodes head orientation in canal-like coordinates, but instead, aligned with the coordinate axes for the Fick strategy (which constrains head torsion). Unilateral stimulation (50 μA, 300 Hz, 200 ms) evoked CW head rotations from the right INC and CCW rotations from the left INC, with variable vertical components. The observed axes of head rotation were consistent with a canal-like coordinate system. Moreover, as predicted, these axes remained fixed in the head, rotating with initial head orientation like the horizontal and torsional axes of a Fick coordinate system. This suggests that the head is ordinarily constrained to zero torsion in Fick coordinates by equally activating CW/CCW populations of neurons in the right/left INC. These data support a simple mechanism for controlling head orientation through the alignment of brain stem neural coordinates with natural behavioral constraints.

The magnetotelluric impedance tensor properties with respect to rotations

Geophysics ◽  
1985 ◽  
Vol 50 (10) ◽  
pp. 1610-1617 ◽  
Author(s):  
Simon Spitz
Keyword(s):  
Data Analysis ◽  
Coordinate System ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Impedance Tensor ◽  
Coordinate Systems ◽  
Magnetotelluric Data ◽  
Conventional Analysis ◽  
Complete Set ◽  
The Relationship

A serious limitation to conventional data analysis is that the data refer mainly to elongated bodies. When three‐dimensional distortions are present, quantitative interpretation based only on the off‐diagonal elements of the conventionally rotated impedance tensor is inadequate, because these off‐diagonal elements are insensitive to the tensor trace. The impedance tensor eigenstate formulation proposed in the literature defines a complete set of parameters suitable for recognition of three‐dimensionality. Generally, though, the eigenvalues do not stand for the off‐diagonal elements of an impedance tensor measured in a physical coordinate system. It is shown how the eigenvalues are modified when the relationship between coordinate system rotations and the eigenstate formulation is clarified. A generalization of the conventional analysis results, but the rotation angle obtained is neither unique nor complete To improve the situation, two new analytical rotation angles are proposed. These angles define two complete intrinsic coordinate systems suitable for magnetotelluric data analysis when a general three‐dimensional structure is involved.

Chinese Geodetic Coordinate System 2000 and its Comparison with WGS84

2014 ◽  
Vol 580-583 ◽  
pp. 2793-2796 ◽  
Author(s):  
Hou Pu Li ◽  
Shao Feng Bian ◽  
Zhong Mei Li
Keyword(s):  
Coordinate System ◽  
Normal Gravity ◽  
Three Dimensional ◽  
Vertical Gradient ◽  
Coordinate Systems ◽  
Present Measurement ◽  
Three Dimensional Coordinate ◽  
Geodetic Coordinate System ◽  
International Measurement ◽  
Geocentric Coordinate System

It is a general trend to adopt the geocentric coordinate system as a geodetic datum for the international measurement community. The definition and realization of Chinese geocentric three-dimensional coordinate system (CGCS2000) which has been employed since July 1st, 2008 were introduced in detail. The defining parameters and derived constants of the reference ellipsoid used were given. The comparison between CGCS2000 and WGS84 was carried out. The differences of geodetic coordinates of a point between the two coordinate systems, normal gravity and vertical gradient of normal gravity on the two ellipsoids caused by the change of the flattening of the ellipsoid were analyzed. The results show that these differences could be neglected in view of present measurement accuracies.

scholarly journals A comparison of three-dimensional rotation formalisms for least-squares and Bayesian inverse kinematics

2021 ◽  
Author(s):  
Ben Serrien ◽  
Klevis Aliaj ◽  
Todd Pataky
Keyword(s):  
Least Squares ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Estimation Error ◽  
Computational Cost ◽  
Three Dimensional ◽  
Linear Least Squares ◽  
Computationally Efficient ◽  
Rotational Degrees Of Freedom ◽  
Value Decomposition

Marker-based inverse kinematics (IK) is prone to errors arising from measurementnoise and soft-tissue artefacts. Various least-squares and Bayesian methods canbe applied to limit the estimation error to a minimum. Recently proposed meth-ods like Bayesian IK come at an increased computational cost however. In thistechnical paper, we present an overview of eight different least squares or BayesianIK methods, including their accuracy and computational load for IK problemsinvolving a single rigid body and three rotational degrees-of-freedom, whose at-titude is estimated from four noisy marker positions. The results indicate thatNon-Linear Least Squares, Variational Bayesian and full Bayesian IK are supe-rior to Singular Value Decomposition in terms of accuracy, with approximatelya two-fold error reduction. However, only Non-Linear Least Squares and Varia-tional Bayesian IK are computationally efficient enough to scale towards practicaluse in biomechanical applications, with computational durations of 1-10 ms; fullyBayesian procedures required approximately 30 s for single rotation calculations.All Python code and supplementary material can be found in this paper’s GitHubrepository: https://github.com/benserrien/pybik.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

2019 ◽  
Vol 11 (1) ◽  
pp. 67-78
Author(s):  
Kamel Meftah ◽  
Lakhdar Sedira
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Field Tensor ◽  
Tetrahedral Element ◽  
Numerical Studies ◽  
Rotational Degrees Of Freedom ◽  
Tensor Approximation

Abstract The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

Novel Design and Three-Dimensional Printing of Variable Stiffness Robotic Grippers

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Yang Yang ◽  
Yonghua Chen ◽  
Ying Wei ◽  
Yingtian Li
Keyword(s):  
3D Printing ◽  
Degrees Of Freedom ◽  
Shape Memory Polymer ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Variable Stiffness ◽  
Analytical Models ◽  
Printing Process ◽  
Finger Joints ◽  
Rotational Degrees Of Freedom

In this paper, a novel robotic gripper design with variable stiffness is proposed and fabricated using a modified additive manufacturing (hereafter called 3D printing) process. The gripper is composed of two identical robotic fingers and each finger has three rotational degrees-of-freedom as inspired by human fingers. The finger design is composed of two materials: acrylonitrile butadiene styrene (ABS) for the bone segments and shape-memory polymer (SMP) for the finger joints. When the SMP joints are exposed to thermal energy and heated to above their glass transition temperature (Tg), the finger joints exhibit very small stiffness, thus allow easy bending by an external force. When there is no bending force, the finger will restore to its original shape thanks to SMP's shape recovering stress. The finger design is actuated by a pneumatics soft actuator. Fabrication of the proposed robotic finger is made possible by a modified 3D printing process. An analytical model is developed to represent the relationship between the soft actuator's air pressure and the finger's deflection angle. Furthermore, analytical modeling of the finger stiffness modulation is presented. Several experiments are conducted to validate the analytical models.

Flight performance and visual control of flight of the free-flying housefly ( Musca domestica L.) I. Organization of the flight motor

1986 ◽  
Vol 312 (1158) ◽  
pp. 527-551 ◽  
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Midsagittal Plane ◽  
Torque Vector ◽  
Translation Velocity ◽  
Flight Motor

Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies’ body axes in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies’ movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly’s midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

Numerical Solution to a Two-Dimensional Conduction Problem Using Rectangular and Cylindrical Body-Fitted Coordinate Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 753-758 ◽  
Author(s):  
A. Goldman ◽  
Y. C. Kao
Keyword(s):  
Temperature Distribution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Two Dimensional ◽  
Coordinate Systems

The temperature distribution in a rectangular plate with a circular void at the center was calculated using a body-fitted coordinate system. Three different transformed geometries were considered: rectangular-rectangular, cut-line, and cylindrical. Problems involving insulated outer surfaces could not be solved using the rectangular-rectangular transformation but could be solved with both the cut-line and cylindrical transformations. The cylindrical transformation also appears to have the capability of being extended to three-dimensional problems.

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