scholarly journals Discussion: “Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers” (Padgaonkar, A. J., Krieger, K. W., and King, A. I., 1975, ASME J. Appl. Mech., 42, pp. 552–556)

1976 ◽  
Vol 43 (2) ◽  
pp. 377-378 ◽  
Author(s):  
Y. King Liu
Keyword(s):  
Rigid Body ◽  
Angular Acceleration

Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements

1979 ◽  
Vol 46 (4) ◽  
pp. 925-930 ◽  
Author(s):  
N. K. Mital ◽  
A. I. King
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Linear Acceleration ◽  
Field Measurements ◽  
Moving Frame ◽  
Accelerometer Data ◽  
Hypothetical Data

The angular acceleration of a rigid body with respect to a body-fixed (moving) frame can be reliably computed from nine acceleration field measurements. Noncommutativity of finite rotations causes computational problems during numerical integration to obtain the transformation matrix, especially when the rotation is three-dimensional and there are errors in the measured linear accelerations. A method based on the orientation vector concept is formulated and tested against hypothetical data. The rigid-body rotations computed from linear accelerometer data from impact acceleration tests are compared against those obtained from three-dimensional analysis of high speed movie films.

scholarly journals Post-Newtonian treatise on the rotational motion of a finite body

1986 ◽  
Vol 114 ◽  
pp. 35-40 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Angular Acceleration ◽  
Relative Magnitude ◽  
The Body ◽  
Coordinate Systems ◽  
Functional Forms ◽  
Finite Body ◽  
The Moment ◽  
Definition Of

The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.

Computation of Rigid-Body Angular Acceleration From Point-Acceleration Measurements

1987 ◽  
Vol 109 (2) ◽  
pp. 124-127 ◽  
Author(s):  
Jorge Angeles
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Measurement Errors ◽  
Angular Acceleration ◽  
The Body ◽  
The Other ◽  
Compatibility Conditions ◽  
Other Hand ◽  
The One

The computation of the angular acceleration of a rigid body from measurements of accelerations of three noncollinear points of the body is presented in this paper. This is based on algorithms presented previously for the computation of the orientation and the angular velocity of a rigid body from measurements of position and velocity of three noncollinear points of the body. Moreover, compatibility conditions that the said point measurements should verify are introduced. These are necessary to verify the rigidity assumption on the one hand; on the other hand, they are introduced as a means of filtering roundoff and/or measurement errors, which is particularly useful if redundant measurements are taken, i.e., on more than three points. The procedure is illustrated with a fully solved example.

Isotropic Accelerometer Strapdowns and Related Algorithms for Rigid-Body Pose and Twist Estimation

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Kalman Filter ◽  
Angular Velocity ◽  
Rigid Body ◽  
Angular Acceleration ◽  
Estimation Algorithm ◽  
Velocity Fields ◽  
Excellent Performance ◽  
Simulation Results ◽  
Novel Design ◽  
Pose And Twist

A novel design of accelerometer strapdown, intended for the estimation of the rigid-body acceleration and velocity fields, is proposed here. The authors introduce the concept of isotropic-polyhedral layout of simplicial biaxial accelerometers (SBA), in which one SBA is rigidly attached at the centroid of each face of the polyhedron. By virtue of both the geometric isotropy of the layout and the structural planar isotropy of the SBA, the point tangential relative acceleration is decoupled from its centripetal counterpart, which is filtered out, along with the angular velocity. The outcome is that the rigid-body angular acceleration can be estimated independent of the angular velocity, thereby overcoming a hurdle that mars the estimation process in current accelerometer strapdowns. An estimation algorithm, based on the extended Kalman filter, is included. Simulation results show an excellent performance of the proposed strapdowns in estimating the acceleration and velocity fields of a moving object along with its pose.

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