Denavit-Hartenberg Parameterization of Euler Angles

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
S. V. Shah ◽  
S. K. Saha ◽  
J. K. Dutt
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Three Dimensional ◽  
Euler Angle ◽  
Euler Angles ◽  
Spherical Joint ◽  
Multiple Degrees Of Freedom ◽  
Cartesian Space ◽  
Revolute Joints

Euler angles describe rotations of a rigid body in three-dimensional Cartesian space, as can be obtained by, say, a spherical joint. The rotation carried out by a spherical joint can also be expressed by using three intersecting revolute joints that can be described using the popular Denavit-Hartenberg (DH) parameters. However, the motions of these revolute joints do not necessarily correspond to any set of the Euler angles. This paper attempts to correlate the Euler angles and DH parameters by introducing a concept of DH parameterization of Euler angels. A systematic approach is presented in order to obtain the DH parameters for any Euler angles set. This gives rise to the concept of Euler-angle-joints (EAJs), which provide rotations equivalent to a particular set of Euler angles. Such EAJs can be conveniently used for the modeling of multibody systems having multiple-degrees-of-freedom joints.

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Quasi-Static Modelling and Computer Simulation of Hanging Cables on Robots

1994 ◽  
Author(s):  
Li-Ping Yang ◽  
Shin-Min Song
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Finite Segment ◽  
Revolute Joints ◽  
Highly Nonlinear ◽  
Finite Segment Method ◽  
Newton Raphson ◽  
Static Modelling ◽  
Parameter Perturbation Method ◽  
Raphson Method

Abstract This paper presents a computer method to simulate the quasi-static motion of hanging cables on robots. The shape of the flexible cable is changing during motion and the finite segment method is applied to determine its configuration. The cable is modeled as a series of rigid segments segments connected together through revolute joints in 2-D case and spherical joints in 3-D case. The elasticity of cable is represented by torsional springs at the joints. In both cases, a set of highly nonlinear equations are derived based on force equilibrium and the Newton-Raphson method is applied to calculate the solution. In order to assure convergence and improve computational efficiency, the parameter perturbation method is applied together with the Newton-Raphson method. Also, some computational strategies are developed to simplify the three dimensional problem. Finally, the developed methods are demonstrated in displaying the motion of a hanging cable which is attached to a revolute joint, a prismatic joint and a three degrees of freedom robot.

Time-varying mesh stiffness calculation for gear pairs with misalignment errors in multiple degrees of freedom based on an analytical method

2021 ◽  
pp. 095440622110392
Author(s):  
Qi Wen ◽  
Qi Chen ◽  
Qungui Du ◽  
Yong Yang
Keyword(s):  
Analytical Model ◽  
Contact Line ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Single Pair ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Position Change ◽  
Multiple Degrees Of Freedom ◽  
Effective Contact

Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) at the mesh position will lead to a change in the time-varying mesh stiffness (TVMS) and then affect the dynamic behaviour of gear pairs. Therefore, a new, more rapid, three-dimensional analytical model for TVMS calculation for gear pairs with three rotational and three translational MEs is established in this paper, and a new solution method based on potential energy theory is presented. In addition, the correctness of the new model is verified by the finite element method (FEM). Moreover, the effective contact line, uneven distribution of mesh force on the contact line, and mesh position change are taken into account. Finally, the TVMS under different ME conditions is calculated with the new analytical model. The results showed that the different MEs have dissimilar effects on the TVMS, and the relationship between the ME and TVMS is nonlinear. In addition, the region of single-pair and double-pair teeth in contact would also change with ME.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface

2011 ◽  
Author(s):  
Chris Salisbury
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Element Analysis ◽  
Revolute Joints ◽  
Stiffness Matrices ◽  
Joint Forces ◽  
Ricatti Equation ◽  
Optimal Dynamic

A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.

Synthesis and analysis of spatial CS-3SS mechanism for body guidance

2015 ◽  
Vol 229 (13) ◽  
pp. 2455-2466
Author(s):  
Wen-Yeuan Chung
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Spherical Joint ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Cylindrical Joint ◽  
Input Parameters ◽  
Three Stages ◽  
Moving Platform

This work presents a new spatial mechanism for three-dimensional body guidance. The moving platform of this mechanism is supported by a C–S leg and three S–S legs. Driving unit is the cylindrical joint and has two input parameters. The strategy for synthesizing the C–S leg is proposed and at most eight positions of the spherical joint can be prescribed, while at most seven positions can be prescribed in designing each S–S leg. This CS-3SS mechanism can thus be synthesized by prescribing at most seven precision poses. For this multi-loop spatial mechanism, both noticeable works that are the analysis of configurations and strategy for evaluating branch defects are carried out. The mechanism by giving two inputs has zero degrees of freedom and is analogous to a spherical kinematic chain with five links. At most eight configurations can be obtained and the criterion of double configurations is derived successfully. These results are based on to develop the strategy for evaluating branch defects. This strategy has three stages which are calculating the values of criteria, checking properties of other branches and final verification. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the proposed mechanism.

Flow-induced patterns in directional solidification: localized morphologies in three-dimensional flows

2000 ◽  
Vol 421 ◽  
pp. 369-380 ◽  
Author(s):  
Y.-J. CHEN ◽  
S. H. DAVIS
Keyword(s):  
Directional Solidification ◽  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Localized States ◽  
Marginal Stability ◽  
Multiple Degrees Of Freedom ◽  
Flow Stagnation ◽  
Moving Front ◽  
Morphological Patterns

We consider the effect of steady, three-dimensional cellular convective fields impressed upon the moving front of a dilute binary alloy in directional solidification. The flows have length scales longer than the characteristic lengths of the morphological instability. A Floquet problem with multiple degrees of freedom in space governs the interfacial dynamics and determines the morphological patterns and marginal stability boundaries. In the cases of weak flows the induced patterns are superpositions of rolls modulated by the forced flows. When the flows are strong, the instability becomes spatially localized and confined at inward flow-stagnation regions on the front. Numerical computations and the WKB method are used to solve the eigenvalue problems, showing various localized states depending on the structures of the imposed flows.

scholarly journals A pathway to desired functionalities in vertically aligned nanocomposites and related architectures

MRS Bulletin ◽  
2021 ◽  
Author(s):  
Aiping Chen ◽  
Quanxi Jia
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interface Microstructure ◽  
Two Dimensional ◽  
Superconducting Properties ◽  
Multiple Degrees Of Freedom ◽  
Challenges And Opportunities ◽  
Vertically Aligned

AbstractEpitaxial vertically aligned nanocomposites (VANs) and their related architectures have shown many intriguing features that are not available from conventional two-dimensional planar multilayers and heterostructures. The ability to control constituent, interface, microstructure, strain, and defects based on VANs has enabled the multiple degrees of freedom to manipulate the optical, magnetic, electrochemical, electronic, ionic, and superconducting properties for specific applications. This field has rapidly expanded from the interest in oxide:oxide to oxide:metal, metal:nitride and nitride:nitride systems. To achieve unparalleled properties of the materials, three-dimensional super-nanocomposites based on a hybrid of VAN and multilayer architectures have been recently explored as well. The challenges and opportunities of VAN films are also discussed in this article.

scholarly journals Three-Dimensional Imaging With Multiple Degrees of Freedom Using Data Fusion

2015 ◽  
Vol 103 (9) ◽  
pp. 1654-1671 ◽  
Author(s):  
Pedro Latorre-Carmona ◽  
Filiberto Pla ◽  
Adrian Stern ◽  
Inkyu Moon ◽  
Bahram Javidi
Keyword(s):  
Data Fusion ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensional Imaging ◽  
Multiple Degrees Of Freedom ◽  
Using Data
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