Estimating the Orientation of a Game Controller Moving in the Vertical Plane Using Inertial Sensors

2012 ◽  
Author(s):  
Peng He ◽  
Philippe Cardou ◽  
André Desbiens
Keyword(s):  
Rigid Body ◽  
Inertial Sensors ◽  
Time Integration ◽  
Vertical Plane ◽  
Nonlinear Function ◽  
Body Motion ◽  
Human Hand ◽  
Game Controller ◽  
State Space Systems ◽  
Novel Method

This paper presents a novel method of estimating the orientation of a rigid body in the vertical plane from point-acceleration measurements, by discerning its gravitational and inertial components. In this method, a simple stochastic model of the human-hand motions is used in order to distinguish between the two types of acceleration. Two mathematical models of the rigid-body motion are formulated as distinct state-space systems, each corresponding to a proposed method. In both two cases, the output is a nonlinear function of the state, which calls for the application of the extended Kalman filter (EKF). The proposed filter is shown to work efficiently through two simulated trajectories, which are representative of human-hand motions. A comparison of the orientation estimates obtained from the proposed method shows that the filter offers more accuracy than a tilt sensor under high accelerations, and avoids the drift obtained by the time-integration of gyroscope measurements.

Vibrations of a Flexible-Link Flexible-Base Robot Arm

2007 ◽  
Author(s):  
Samir E. Emam
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Natural Frequencies ◽  
Vertical Plane ◽  
Vertical Direction ◽  
Body Motion ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Robot Arm ◽  
Lumped Mass

Dynamics and vibrations of flexible robot arms have received considerable attention in recent years. The flexibility of the arm affects the function of the robot and complicates its dynamics as well. Generally, the base of the robot arm has some elasticity, which also affects the precision of its function. We model the robot arm as a flexible beam moving in a vertical plane and resting on two springs: one is in the vertical direction and the other one is in the rotational direction. A lumped mass, which simulates the payload, is attached to the tip of the beam. The beam translates and rotates as a rigid body and moreover it deforms in the lateral direction. The extended Hamilton principle is used to derive the governing equations of motion and their corresponding boundary conditions. We obtained three coupled differential equations: two ordinary-differential equations governing the rigid-body motion of the arm and a partial differential equation governing its deformation. An exact solution for the natural frequencies and mode shapes of the vibrations of the arm about an equilibrium position is obtained. The significance of the effect of the flexibility of the link and the base and the ratio of the mass at the tip point to the mass of the beam on the natural frequencies and mode shapes is investigated.

Approximation of Finite Rigid Body Motions

2009 ◽  
Author(s):  
Andreas Mu¨ller
Keyword(s):  
Rigid Body ◽  
Euler Equations ◽  
Time Derivative ◽  
Time Integration ◽  
Body Motion ◽  
Motion Group ◽  
Time Stepping ◽  
Approximation Formulas ◽  
Rigid Body Motions ◽  
Local Parameters

It is well-known that there is no integrable relation between the twist of a rigid body and its finite motion, since the angular velocity components are non-holonomic velocity coordinates. Moreover, the reconstruction of the body’s motion requires to solve a set of differential equations on the rigid body motion group. This is usually avoided by introducing local parameters (e.g. Euler angles) so that the problem becomes an ordinary differential equation on a vector space (e.g. kinematic Euler equations). In this paper the original problem on the motion group is treated. A family of approximation formulas is presented that allow reconstructing large rigid body motions from a given velocity field up to a desired order. It is shown that a k-th order accurate reconstruction requires the first k – 1 time derivative of the velocity. As an application the reconstruction formulas are used for the rotation update in a momentum preserving time stepping scheme for time integration of the dynamic Euler equations.

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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