New kinematic parameters of the finite rotation of a rigid body

2013 ◽  
Vol 77 (4) ◽  
pp. 380-385
Author(s):  
S. Ye. Perelyayev
Keyword(s):  
Rigid Body ◽  
Finite Rotation ◽  
Kinematic Parameters

The New Analytical Algorithm for Determining the Strapdown INS Orientation

2019 ◽  
Vol 20 (10) ◽  
pp. 624-628 ◽  
Author(s):  
A. V. Molodenkov ◽  
Ya. G. Sapunkov ◽  
T. V. Molodenkova
Keyword(s):  
Angular Velocity ◽  
Analytical Solution ◽  
Rigid Body ◽  
Linear Equation ◽  
Initial Position ◽  
Finite Rotation ◽  
Zero Initial Condition ◽  
Analytical Algorithm ◽  
Subsequent Step ◽  
Regular Character

The analytical solution of an approximate (truncated) equation for the vector of a rigid body finite rotation has made it possible to solve the problem of determining the quaternion of orientation of a rigid body for an arbitrary angular velocity and small angle of rotation of a rigid body with the help of quadratures. Proceeding from this solution, the following approach to the construction of the new analytical algorithm for computation of a rigid body orientation with the use of strapdown INS is proposed: 1) By the set components of the angular velocity of a rigid body on the basis of mutually — unambiguous changes of the variables at each time point, a new angular velocity of a rigid body is calculated; 2) Using the new angular velocity and the initial position of a rigid body, with the help of the quadratures we find the exact solution of an approximate linear equation for the vector of a rigid body finite rotation with a zero initial condition; 3) The value of the quaternion orientation of a rigid body (strapdown INS) is determined by the vector of finite rotation. During construction of the algorithm for strapdown INS orientation at each subsequent step the change of the variables takes into account the previous step of the algorithm in such a way that each time the initial value of the vector of finite rotation of a rigid body will be equal to zero. Since the proposed algorithm for the analytical solution of the approximate linear equation for the vector of finite rotation is exact, it has a regular character for all angular motions of a rigid body).

On the Synthesis of Three-Poses Rigid-Body Guidance Mechanisms

2015 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea
Keyword(s):  
Rigid Body ◽  
Finite Rotation ◽  
Graphical Approach ◽  
Kinematic Characteristics ◽  
Different Types

A graphical approach that is based on the use of the pole triangle among the three poles of the finite rotation, along with its circumcircle and those of the three image pole triangles, which intersect each other at the orthocenter of the pole triangle, is presented in this paper. This method is applied and parameterized in SolidWorks to synthesize different types of mechanisms for any triple of prescribed positions, as four-bar linkages (4R), slider-crank/rocker mechanisms (3RP), double-sliders (2R2P), guiding mechanisms (RPRP). Finally, the kinematic characteristics of the rigid-body guidance mechanisms for three finitely and infinitesimally separated positions are compared via significant examples.

Applications of the 4D Geometric Algebra to Dimensional Mobility Criteria of Delassus-Parallelogram and Bennett Paradoxical Linkages

2015 ◽  
Author(s):  
Chung-Ching Lee
Keyword(s):  
Rigid Body ◽  
Geometric Algebra ◽  
Three Dimensional ◽  
Grassmann Algebra ◽  
Body Motion ◽  
Finite Rotation ◽  
Finite Rotations ◽  
Hypercomplex Number ◽  
Geometric Problems ◽  
Methodical Approach

Geometric algebra is also termed Clifford-Grassmann algebra or hypercomplex number. It allows studying space geometric problems in an easy and compact way. Transforming three-dimensional (3D) Euclidean geometric entities to actual elements of four-dimensional (4D) geometric algebra (abbreviated to g4) through a methodical approach of geometric algebra, one can describe motion displacements as even elements of g4. This article relies on the combined rotation and translation in g4 to establish the dimensional constraints of two non-exceptional overconstrained paradoxical linkages. Firstly, fundamentals of geometric algebra are recalled. Then, the single finite rotation and the composition of two successive finite rotations are introduced. After that, a general rigid-body motion in g4 is revealed for a possible application in exploring paradoxical chains using the geometric algebra. Finally, the metric or dimensional mobility criteria of Delassus-parallelogram four-screw and Bennett four-revolute paradoxical linkages are algebraically verified.

Attitude Determination by External Vectors in Airplane Free Spin Investigation

2020 ◽  
Vol 28 (3) ◽  
pp. 43-59
Author(s):  
A.V. Vyalkov ◽  
Keyword(s):  
Attitude Determination ◽  
Vertical Wind ◽  
Rotation Vector ◽  
Finite Rotation ◽  
Kinematic Parameters ◽  
Body Frame ◽  
Aircraft Model ◽  
External Reference

The article gives an overview of the methods for determining orientation angles from observations of external reference vectors. To maintain the observability of the kinematic parameters of the free-flying aircraft model motion in a vertical wind tun-nel, we analyzed the methods for determining the finite rotation vector using two, three or more vectors, known in a model body frame, as well as their derivatives. The methods to estimate the reliability of the calculated orientation angles are proposed. The method for estimating the radius of the free-flying model spin is considered.

An Algorithm for the Workspace of a General n-R Robot

1983 ◽  
Vol 105 (1) ◽  
pp. 52-57 ◽  
Author(s):  
Y. C. Tsai ◽  
A. H. Soni
Keyword(s):  
Rigid Body ◽  
Coordinate Transformation ◽  
Linear Optimization ◽  
Optimization Technique ◽  
Robot Hand ◽  
Kinematic Parameters ◽  
Arbitrary Plane

An algorithm is developed to determine the workspace on an arbitrary plane for an n-R robot. The algorithm is based on a linear optimization technique and on small incremental displacements applied to coordinate transformation equations relating the kinematic parameters of the n-R robot. The algorithm provides flexibility to let the user treat the robot hand as a point, a line, or a rigid-body. The revolute pairs of the robot may execute full or partial rotation. The proposed method may be extended to incorporate in a robot the existence of prismatic pairs along with revolute pairs.

Articulatory Behavior Pre and Post Full-Mouth Tooth Extraction and Alveoloplasty

1980 ◽  
Vol 23 (3) ◽  
pp. 630-645 ◽  
Author(s):  
Gerald Zimmermann ◽  
J.A. Scott Kelso ◽  
Larry Lander
Keyword(s):  
Control Subject ◽  
High Speed ◽  
Tooth Extraction ◽  
Kinematic Parameters ◽  
Experimental Conditions ◽  
Mean Values ◽  
Articulatory Movements ◽  
The Mean ◽  
Experimental Subjects ◽  
Normal Speech

High speed cinefluorography was used to track articulatory movements preceding and following full-mouth tooth extraction and alveoloplasty in two subjects. Films also were made of a control subject on two separate days. The purpose of the study was to determine the effects of dramatically altering the structural dimensions of the oral cavity on the kinematic parameters of speech. The results showed that the experimental subjects performed differently pre and postoperatively though the changes were in different directions for the two subjects. Differences in both means and variabilities of kinematic parameters were larger between days for the experimental (operated) subjects than for the control subject. The results for the Control subject also showed significant differences in the mean values of kinematic variables between days though these day-to-day differences could not account for the effects found pre- and postoperatively. The results of the kinematic analysis, particularly the finding that transition time was most stable over the experimental conditions for the operated subjects, are used to speculate about the coordination of normal speech.

Dance teachers’ aesthetic perception of kinematic parameters.

2015 ◽  
Vol 9 (4) ◽  
pp. 442-450 ◽  
Author(s):  
Carlota Torrents ◽  
Marta Castañer ◽  
Ferran Reverter ◽  
Gaspar Morey ◽  
Toni Jofre
Keyword(s):  
Aesthetic Perception ◽  
Kinematic Parameters ◽  
Dance Teachers
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