Application of Dual Quaternions to the Study of Gyrodynamics

1967 ◽  
Vol 89 (1) ◽  
pp. 137-143 ◽  
Author(s):  
A. T. Yang
Keyword(s):  
Equations Of Motion ◽  
Degree Of Freedom ◽  
System Dynamic ◽  
Dynamic Equations ◽  
Dual Quaternions ◽  
Special Cases ◽  
Six Degree Of Freedom

Dual quaternions are used to derive equations of motion for an offset unsymmetrical gyroscope. From the equations, in view of the general characteristics of this six-degree-of-freedom system, dynamic equations for a variety of gyroscopic and pendulous systems may be deduced as special cases. Examples are given for illustration.

Analysis of an Offset Unsymmetric Gyroscope With Oblique Rotor Using (3×3) Matrices With Dual-Number Elements

1969 ◽  
Vol 91 (3) ◽  
pp. 535-541 ◽  
Author(s):  
An Tzu Yang
Keyword(s):  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Spin Axis ◽  
Dynamic Equations ◽  
Gyroscopic System ◽  
Dual Number ◽  
System A ◽  
Six Degree Of Freedom ◽  
Special Case

Using 3 × 3 matrices of dual-number elements, dynamic equations are obtained for an offset unsymmetric gyroscope with obliquely placed rotor, a generalized six-degree-of-freedom gyroscopic system (shown schematically in Fig. 3). Equations of motion for a special case of the system, a two-frame symmetric gyroscope, conventional in all aspects except the rotor is inclined relative to its spin axis, are deduced; these equations are applied to the study of the effects of a slightly inclined rotor on (a) a two-frame symmetric gyroscope in steady precession and (b) a Faucualt’s gyrocompass.

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.

Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods

1985 ◽  
Vol 107 (2) ◽  
pp. 189-200 ◽  
Author(s):  
L.-W. Tsai ◽  
A. P. Morgan
Keyword(s):  
Polynomial Equation ◽  
Partial Solution ◽  
Degree Of Freedom ◽  
Continuation Methods ◽  
Hand Position ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Prismatic Joints ◽  
Six Degree Of Freedom ◽  
Second Degree

This paper presents a unique approach to the kinematic analysis of the most general six-degree-of-freedom, six-revolute-joint manipulators. Previously, the problem of computing all possible configurations of a manipulator corresponding to a given hand position was approached by reducing the problem to that of solving a high degree polynomial equation in one variable. In this paper it is shown that the problem can be reduced to that of solving a system of eight second-degree equations in eight unknowns. It is further demonstrated that this second-degree system can be routinely solved using a continuation algorithm. To complete the general analysis, a second numerical method—a continuation heuristic—is shown to generate partial solution sets quickly. Finally, in some special cases, closed form solutions were obtained for some commonly used industrial manipulators. The results can be applied to the analysis of both six and five-degree-of-freedom manipulators composed of mixed revolute and prismatic joints. The numerical stability of continuation on small second-degree systems opens the way for routine use in offline robot programming applications.

Trajectory Generation for Three-Degree-of-Freedom Cable-Suspended Parallel Robots Based on Analytical Integration of the Dynamic Equations

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Xiaoling Jiang ◽  
Clément Gosselin
Keyword(s):  
Differential Equations ◽  
Trajectory Generation ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Dynamic Equations ◽  
Special Cases ◽  
Linear Differential ◽  
Pass Through ◽  
Cable Forces ◽  
Three Degree Of Freedom

This paper proposes a trajectory generation technique for three degree-of-freedom (3-dof) planar cable-suspended parallel robots. Based on the kinematic and dynamic modeling of the robot, positive constant ratios between cable tensions and cable lengths are assumed. This assumption allows the transformation of the dynamic equations into linear differential equations with constant coefficients for the positioning part, while the orientation equation becomes a pendulum-like differential equation for which accurate solutions can be found in the literature. The integration of the differential equations is shown to yield families of translational trajectories and associated special frequencies. This result generalizes the special cases previously identified in the literature. Combining the results obtained with translational trajectories and rotational trajectories, more general combined motions are analyzed. Examples are given in order to demonstrate the results. Because of the initial assumption on which the proposed method is based, the ratio between cable forces and cable lengths is constant and hence always positive, which ensures that all cables remain under tension. Therefore, the acceleration vector remains in the column space of the Jacobian matrix, which means that the mechanism can smoothly pass through kinematic singularities. The proposed trajectory planning approach can be used to plan dynamic trajectories that extend beyond the static workspace of the mechanism.

The Dynamics of Ball Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 1-10 ◽  
Author(s):  
C. T. Walters
Keyword(s):  
Fourth Order ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Spin Axis ◽  
General Analysis ◽  
Ball Bearings ◽  
High Speeds ◽  
Six Degree Of Freedom

The details of the dynamics of the elements of a ball bearing become increasingly important at high speeds. A comprehensive general analysis of the motions of balls and a ball separator with realistic lubrication is summarized. The equations of motion consider four degree-of-freedom balls and a six degree-of-freedom separator and are integrated numerically with a fourth order Runge Kutta scheme. Numerical results are presented for a particular spin axis gyro bearing configuration.

scholarly journals Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1850-1868 ◽  
Author(s):  
A. Weiss ◽  
R. G. Langlois ◽  
M. J. D. Hayes
Keyword(s):  
Rotational Motion ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Design Tool ◽  
Degree Of Freedom ◽  
Rigid Sphere ◽  
Motion Platform ◽  
Six Degree Of Freedom ◽  
Dynamics And Vibration ◽  
Omnidirectional Wheels

SUMMARYThis paper presents analysis of the dynamics and vibration of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The purpose of the analysis is to serve as a design tool for the construction of a six-degree-of-freedom motion platform with unlimited rotational motion. The equations of motion are presented taking flexibility of the system into account. The behaviour of the system is illustrated by sample configurations with a range of omnidirectional wheel types and geometries. Vibration analysis follows, and sensitivity to various parameters is investigated. It is determined that the geometry of omnidirectional wheels has a significant effect on the behaviour of the system.

Closed-Form Forward Dynamic Equations of 6-DOF PUS Type Parallel Manipulators

2000 ◽  
Author(s):  
Jong-Phil Kim ◽  
Jeha Ryu
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Simulation Software ◽  
Dynamic Equations ◽  
Constant Length ◽  
Euler Approach ◽  
Six Degree Of Freedom

Abstract This paper presents closed-form forward dynamic equations of six degree-of-freedom HexaSlide type parallel manipulators. The HexaSlide type parallel manipulators are characterized by an architecture with constant-length links that are attached to moving sliders on the ground and to a mobile platform. Based on the kinematic analysis, forward dynamic equations of motion of the parallel manipulator are derived by the Newton-Euler approach. In this derivation, joint frictions as well as all link inertia are included. The correctness of derived dynamic equations is validated by a commercial dynamic simulation software. The kinematic and dynamic equations may be used in the computer simulation of various control strategies.

Dynamic Modeling of a Six Degree-of-Freedom Flight Simulator Motion Base

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Mauricio Becerra-Vargas ◽  
Eduardo Morgado Belo
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Kinematic Model ◽  
Closed Form Solution ◽  
Stewart Platform ◽  
Degree Of Freedom ◽  
Dynamic Equations ◽  
Flight Simulator ◽  
Simulator Motion ◽  
Six Degree Of Freedom

This paper presents a closed-form solution for the direct dynamic model of a flight simulator motion base. The motion base consists of a six degree-of-freedom (6DOF) Stewart platform robotic manipulator driven by electromechanical actuators. The dynamic model is derived using the Newton–Euler method. Our derivation is closed to that of Dasgupta and Mruthyunjaya (1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012), however, we give some insights into the structure and properties of those equations, i.e., a kinematic model of the universal joint, inclusion of electromechanical actuator dynamics and the full dynamic equations in matrix form in terms of Euler angles and platform position vector. These expressions are interesting for control, simulation, and design of flight simulators motion bases. Development of a inverse dynamic control law by using coefficients matrices of dynamic equation and real aircraft trajectories are implemented and simulation results are also presented.

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

Sign in / Sign up

Export Citation Format

Share Document