A Polynomial Approach to Inverse Kinematics of Rolling Contact

2012 ◽  
Author(s):  
Lei Cui ◽  
Jian S. Dai
Keyword(s):  
Differential Equations ◽  
Velocity Profile ◽  
Open Source Software ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Rolling Contact ◽  
Moving Object ◽  
Nonlinear Ordinary Differential Equations ◽  
Rotational Degrees Of Freedom ◽  
Polynomial Formulation

A moving object has three rotational degrees of freedom with respect to the fixed one when the two objects maintain rolling contact. Thus three kinematic inputs are considered necessary for the moving object to follow a trajectory described by its velocity profile as function of time. This paper formulates the problem as a system of three nonlinear equations and reduces it to solving a polynomial of degree six with one variable. This leads to fast and accurate numerical approximations of roots on a computer either by commercial software or open-source software. This polynomial formulation is different from previous ones that require solving a system of nonlinear ordinary differential equations.

A Polynomial Formulation of Inverse Kinematics of Rolling Contact

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Lei Cui ◽  
Jian S. Dai
Keyword(s):  
Degrees Of Freedom ◽  
Contact Point ◽  
Rolling Contact ◽  
Moving Object ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Univariate Polynomial ◽  
Curvature Theory ◽  
Robotic Devices ◽  
Polynomial Formulation

Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed to derive three kinematic inputs required for the moving object to follow a trajectory described by its velocity profile when the moving object has three rotational DOFs and thus can rotate about any axis through the contact point with respect to the fixed object. We obtained three contact equations in the form of a system of three nonlinear algebraic equations by applying the curvature theory in differential geometry and simplified the three nonlinear algebraic equations to a univariate polynomial of degree six. Differing from the existing solution that requires solving a system of nonlinear ordinary differential equations, this polynomial is suitable for fast and accurate numerical root approximations. The contact equations further revealed the two essential parts of the spin velocity: The induced spin velocity governed by the geometry and the compensatory spin velocity provided externally to realize the desired spin velocity.

scholarly journals A comparison of three-dimensional rotation formalisms for least-squares and Bayesian inverse kinematics

2021 ◽  
Author(s):  
Ben Serrien ◽  
Klevis Aliaj ◽  
Todd Pataky
Keyword(s):  
Least Squares ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Estimation Error ◽  
Computational Cost ◽  
Three Dimensional ◽  
Linear Least Squares ◽  
Computationally Efficient ◽  
Rotational Degrees Of Freedom ◽  
Value Decomposition

Marker-based inverse kinematics (IK) is prone to errors arising from measurementnoise and soft-tissue artefacts. Various least-squares and Bayesian methods canbe applied to limit the estimation error to a minimum. Recently proposed meth-ods like Bayesian IK come at an increased computational cost however. In thistechnical paper, we present an overview of eight different least squares or BayesianIK methods, including their accuracy and computational load for IK problemsinvolving a single rigid body and three rotational degrees-of-freedom, whose at-titude is estimated from four noisy marker positions. The results indicate thatNon-Linear Least Squares, Variational Bayesian and full Bayesian IK are supe-rior to Singular Value Decomposition in terms of accuracy, with approximatelya two-fold error reduction. However, only Non-Linear Least Squares and Varia-tional Bayesian IK are computationally efficient enough to scale towards practicaluse in biomechanical applications, with computational durations of 1-10 ms; fullyBayesian procedures required approximately 30 s for single rotation calculations.All Python code and supplementary material can be found in this paper’s GitHubrepository: https://github.com/benserrien/pybik.

In-hand forward and inverse kinematics with rolling contact

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2381-2399 ◽  
Author(s):  
Lei Cui ◽  
Jie Sun ◽  
Jian S. Dai
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Rolling Contact ◽  
Moving Frame ◽  
Robot Hand ◽  
Robotic Hands ◽  
Geometric Framework ◽  
Univariate Polynomial ◽  
Forward And Inverse Kinematics ◽  
Exponential Formula

SUMMARYRobotic hands use rolling contact to manipulate a grasped object to a desired location, even when the finger and the palm linkage mechanisms lack degrees of freedom. This paper presents a systematic approach to the forward and inverse kinematics of in-hand manipulation. The moving frame method in differential geometry is integrated into the product of exponential formula to establish a pure geometric framework of the kinematics of a robot hand. The forward and inverse kinematics of a multifingered hand are obtained in terms of the joint rates and contact trajectories. A two-fingered planar robot hand and a three-fingered spatial robot hand are used to demonstrate the proposed approach. The proposed formulation amounts to solving a univariate polynomial, providing an alternative to the existing ones that require numerical integration.

scholarly journals Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

2019 ◽  
Vol 15 (1) ◽  
pp. 66-80
Author(s):  
Xiaodong Jin ◽  
Yuefa Fang ◽  
Dan Zhang ◽  
Xueling Luo
Keyword(s):  
Machine Tools ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Rotational Axis ◽  
Revolute Joints ◽  
3D Printers ◽  
Rotational Degrees Of Freedom ◽  
Moving Platform ◽  
Orientation Workspace

AbstractThe parallel spindle heads with high rotational capability are demanded in the area of multi-axis machine tools and 3D printers. This paper focuses on designing a class of 2R1T (R: Rotation; T: Translation) parallel spindle heads and the corresponding collaborative 5-axis manipulators with 2-dimension (2D) large rotational angles. In order to construct 2D rotational degrees of freedom (DOFs), a platform with 2D revolute joints is proposed first. Based on the constraint screw theory, the feasible limbs that can be connected in the platform are synthesized. In order to provide constant rotational axis for the platform, a class of redundant limbs are designed. A class of redundant 2R1T parallel spindle heads is obtained by connecting the redundant limbs with the platform and the redundant characteristics are verified by the modified Grübler-Kutzbach criterion. The corresponding 5-axis collaborative manipulators are presented by constructing a 2-DOF series translational bottom moving platform. The inverse kinematics and the orientation workspace as well as the decoupling characteristics of this type of 2R1T parallel spindle heads are analyzed. The results show that these manipulators have large 2D rotational angles than the traditional A3/Z3 heads and can be potentially used in the application of multi-axis machine tools and the 3D printers.

scholarly journals Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force

2020 ◽  
Vol 9 (1) ◽  
pp. 398-411 ◽  
Author(s):  
Abayomi S. Oke ◽  
Winifred N. Mutuku ◽  
Mark Kimathi ◽  
Isaac L. Animasaun
Keyword(s):  
Differential Equations ◽  
Velocity Profile ◽  
Ordinary Differential Equations ◽  
Coriolis Force ◽  
Dynamic Viscosity ◽  
Stokes Equations ◽  
Fluid Model ◽  
Casson Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Casson Fluid Model

AbstractCasson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x-direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z-direction.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

Effects of Dynamic Model Errors in Task-Priority Operational Space Control

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Paolo Di Lillo ◽  
Gianluca Antonelli ◽  
Ciro Natale
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Null Space ◽  
Control Algorithms ◽  
Model Errors ◽  
Operational Space ◽  
Dynamic Level ◽  
Concurrent Tasks ◽  
Modeling Errors

SUMMARY Control algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

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