Transformation Matrices

2021 ◽  
pp. 127-156
Author(s):  
Steve Marschner ◽  
Peter Shirley
Keyword(s):  
Transformation Matrices

scholarly journals Reference in-vitro dataset for inertial-sensor-to-bone alignment applied to the tibiofemoral joint

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ive Weygers ◽  
Manon Kok ◽  
Thomas Seel ◽  
Darshan Shah ◽  
Orçun Taylan ◽  
...  
Keyword(s):  
Inertial Sensors ◽  
Inertial Sensor ◽  
Ground Truth ◽  
Transformation Matrices ◽  
True Model ◽  
Advance Research ◽  
Manual Palpation ◽  
Visualization Tools ◽  
Inertial Measurements

AbstractSkin-attached inertial sensors are increasingly used for kinematic analysis. However, their ability to measure outside-lab can only be exploited after correctly aligning the sensor axes with the underlying anatomical axes. Emerging model-based inertial-sensor-to-bone alignment methods relate inertial measurements with a model of the joint to overcome calibration movements and sensor placement assumptions. It is unclear how good such alignment methods can identify the anatomical axes. Any misalignment results in kinematic cross-talk errors, which makes model validation and the interpretation of the resulting kinematics measurements challenging. This study provides an anatomically correct ground-truth reference dataset from dynamic motions on a cadaver. In contrast with existing references, this enables a true model evaluation that overcomes influences from soft-tissue artifacts, orientation and manual palpation errors. This dataset comprises extensive dynamic movements that are recorded with multimodal measurements including trajectories of optical and virtual (via computed tomography) anatomical markers, reference kinematics, inertial measurements, transformation matrices and visualization tools. The dataset can be used either as a ground-truth reference or to advance research in inertial-sensor-to-bone-alignment.

Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses

1994 ◽  
Vol 116 (2) ◽  
pp. 614-621 ◽  
Author(s):  
Yong-Xian Xu ◽  
D. Kohli ◽  
Tzu-Chen Weng
Keyword(s):  
Stability Index ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Singularity ◽  
Numerical Examples ◽  
Transformation Matrices ◽  
Unstable Configuration ◽  
Direct Kinematics

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

Mechanical Alignment Using Duplicate Circular Wedges

1999 ◽  
Vol 121 (2) ◽  
pp. 305-309
Author(s):  
J. F. Ca´rdenas-Garci´a ◽  
K. P. Suryanarayan ◽  
W. E. Ingalls
Keyword(s):  
Wedge Angle ◽  
Mechanical Alignment ◽  
Transformation Matrices ◽  
The Asymmetry ◽  
Mechanical Components ◽  
Kinematic Transformation

There is a need for the repeatable, accurate, precise and versatile alignment of mechanical components. A flexible and inexpensive approach to this problem is the use of a duplicate pair of wedged discs. This paper uses kinematic transformation matrices to examine in detail the design of such a wedge pair. The accuracy, precision and versatility of the circular wedges are shown to be functions of wedge angle, the number of positions or increments along the circumference of the circular wedge, and changes in the offset angle, which defines the asymmetry of the discs.

A UNIFIED FORMALISM OF THERMAL QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (14) ◽  
pp. 2363-2409 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Polarization ◽  
Time Dependent ◽  
Quantum Field ◽  
Bogoliubov Transformation ◽  
Transformation Matrices ◽  
Thermo Field Dynamics ◽  
The Matrix ◽  
Recent Developments

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

Transformation Matrices

2018 ◽  
pp. 109-138
Author(s):  
Steve Marschner ◽  
Peter Shirley ◽  
Michael Ashikhmin ◽  
Michael Gleicher ◽  
Naty Hoffman ◽  
...  
Keyword(s):  
Transformation Matrices

scholarly journals A New Approach to the Solution of Robot Kinematics Based on Relative Transformation Matrices

2016 ◽  
Vol 5 (3) ◽  
pp. 213
Author(s):  
Mohammad Reza Elhami ◽  
Iman Dashti
Keyword(s):  
Robot Manipulator ◽  
Robot Kinematics ◽  
Coordinate Frame ◽  
End Effector ◽  
New Approach ◽  
Transformation Matrices ◽  
The World ◽  
Convenient Approach ◽  
Position And Orientation ◽  
Relative Transformation

In analyzing robot manipulator kinematics, we need to describe relative movement of adjacent linkages or joints in order to obtain the pose of end effector (both position and orientation) in reference coordinate frame. Denavit-Hartenberg established a method based on a 4×4 homogenous matrix so called “A” matrix. This method used by most of the authors for kinematics and dynamic analysis of the robot manipulators. Although it has many advantages, however, finding the elements of this matrix and link/joint’s parameters is sometimes complicated and confusing. By considering these difficulties, the authors proposed a new approach called ‘convenient approach’ that is developed based on “Relative Transformations Principle”. It provides a very simple and convenient way for the solution of robot kinematics compared to the conventional D-H representation. In order to clarify this point, the kinematics of the world known Stanford manipulator has been solved through D-H representation as well as convenient approach and the results are compared.

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