Series-Chain Planar Manipulators: Inertial Singularities

1993 ◽  
Vol 115 (4) ◽  
pp. 941-945 ◽  
Author(s):  
S. K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Mechanical System ◽  
Dynamic Behavior ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Dynamic Equations ◽  
Numerical Errors ◽  
Inertia Matrix ◽  
Planar Manipulators ◽  
Prismatic Joints

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation of their dynamic equations. An important step in the simulation is the inversion of a matrix, often known as the inertia matrix of the system. In the configurations, where the inertia matrix is singular, the simulation is prone to large numerical errors. Commonly, it is believed that this inertia matrix is always positive definite (or, nonsingular) no matter what geometric and inertial attributes are assigned to the links. In this paper, we show that the inertia matrix of a multi-degree-of-freedom mechanical system modeled with point masses can be singular at special configurations of the links. We present a way to systematically enumerate some of these configurations where the inertia matrix for planar series-chain manipulators built with revolute and prismatic joints are singular.

Inertia Matrix Singularity of Series-Chain Spatial Manipulators With Point Masses

1993 ◽  
Vol 115 (4) ◽  
pp. 723-725 ◽  
Author(s):  
Sunil K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Dynamic Behavior ◽  
Mechanical Systems ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Numerical Errors ◽  
Singular Configurations ◽  
Spatial Series ◽  
Inertia Matrix ◽  
Incomplete Models

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation. An important step in this simulation is the inversion of inertia matrix of the system. In singular configurations of the inertia matrix, the simulation is prone to large numerical errors. Usually, it is believed that an inertia matrix is always positive definite. In this paper, it is shown that for spatial series-chain manipulators, when the links are modeled as point masses, a multitude of configurations exists when the inertia matrix becomes singular. These singularities arise because point masses lead to incomplete models of the system.

Structure Damage Detection via the Behavior of Substructure

1991 ◽  
Author(s):  
J. H. Wang ◽  
C. S. Liou
Keyword(s):  
Damage Detection ◽  
Mechanical System ◽  
Dynamic Behavior ◽  
Structural Damage ◽  
Structure Damage

Abstract A mechanical system generally consists of many substructures. However, it is impossible to observe the dynamic behavior of any substructure directly when the whole structure is in operation. A method was proposed in this work to determine the FRFs of a substructure by using the measured FRFs of the whole structure and the priorly known FRFs of another substructure With this method, one can detect the structural damage more easily by observing the change of the FRFs of the damaged substructure.

The Physical and Computer Modeling of Plastic Deformation of Low Carbon Steel in Semisolid State

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Marcin Hojny ◽  
Miroslaw Glowacki
Keyword(s):  
Computer Simulation ◽  
Low Carbon Steel ◽  
Mass Conservation ◽  
Analytical Form ◽  
Plastic Behavior ◽  
Volume Loss ◽  
Low Carbon ◽  
Compression Tests ◽  
Thermomechanical Model ◽  
Numerical Errors

This paper reports the results of theoretical and experimental work leading to the construction of a dedicated finite element method (FEM) system allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for integrated casting and rolling of steel processes, which was equipped with graphical, database oriented pre- and postprocessing. The kernel of the system is a numerical FEM solver based on a coupled thermomechanical model with changing density and mass conservation condition given in analytical form. The system was also equipped with an inverse analysis module having crucial significance for interpretation of results of compression tests at temperatures close to the solidus level. One of the advantages of the solution is the negligible volume loss of the deformation zone due to the analytical form of mass conservation conditions. This prevents FEM variational solution from unintentional specimen volume loss caused by numerical errors, which is inevitable in cases where the condition is written in its numerical form. It is very important for the computer simulation of deformation processes to be running at temperatures characteristic of the last stage of solidification. The still existing density change in mushy steel causes volume changes comparable to those caused by numerical errors. This paper reports work concerning the adaptation of the model to simulation of plastic behavior of axial-symmetrical steel samples subjected to compression at temperature levels higher than 1400°C. The emphasis is placed on the computer aided testing procedure leading to the determination of mechanical properties of steels at temperatures that are very close to the solidus line. Example results of computer simulation using the developed system are presented as well.

FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES

2005 ◽  
Vol 29 (3) ◽  
pp. 343-356 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Dimensional Space ◽  
Parallel Manipulators ◽  
End Effector ◽  
Input And Output ◽  
Planar Manipulators ◽  
Order Polynomial ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

Landing efficiency control of a six-degree-of-freedom aircraft model with magnetorheological dampers: Part 1—Modeling

2020 ◽  
pp. 1045389X2094257
Author(s):  
Byung-Hyuk Kang ◽  
Ji-Young Yoon ◽  
Gi-Woo Kim ◽  
Seung-Bok Choi
Keyword(s):  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Magnetorheological Damper ◽  
Dynamic Equations ◽  
Design Parameters ◽  
Coordinate Frame ◽  
Aircraft Model ◽  
Efficiency Control ◽  
Six Degree Of Freedom ◽  
Principal Design

This work presents landing efficiency control of a six-degree-of-freedom aircraft model, which has a controllable landing gear system with magnetorheological damper. Due to lengthy contents, this work is divided into two parts. In Part 1, both the kinematic and dynamic equations of the six-degree-of-freedom aircraft model are derived. After determining the principal design parameters of magnetorheological damper based on commercial Beechcraft Baron B55 (passive oleo-strut type) damper, the kinematic equations are derived using the aircraft body coordinate frame and homogeneous coordinates of the reference frame, while the dynamic equations are derived using Euler–Lagrange equation to represent the heave, roll, and pitch motions of the aircraft model. In Part 2, the landing performance based on landing efficiencies is analyzed through the landing motions using various controllers.

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