First- and Second-Order Kinematics-Based Constraint System Analysis and Reconfiguration Identification for the Queer-Square Mechanism

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xi Kang ◽  
Xinsheng Zhang ◽  
Jian S. Dai
Keyword(s):  
Configuration Space ◽  
Bilinear Form ◽  
System Analysis ◽  
Kinematic Model ◽  
Second Order ◽  
Constraint System ◽  
Lie Bracket ◽  
Geometric Conditions ◽  
Reconfigurable Mechanisms ◽  
Order Constraints

Reconfiguration identification of a mechanism is essential in design and analysis of reconfigurable mechanisms. However, reconfiguration identification of a multiloop reconfigurable mechanism is still a challenge. This paper establishes the first- and second-order kinematic model in the queer-square mechanism to obtain the constraint system by using the sequential operation of the Lie bracket in a bilinear form. Introducing a bilinear form to reduce the complexity of first- and second-order constraints, the constraint system with first- and second-order kinematics of the queer-square mechanism is attained in a simplified form. By obtaining the solutions of the constraint system, six motion branches of the queer-square mechanism are identified and their corresponding geometric conditions are presented. Moreover, the initial configuration space of the mechanism is obtained.

Development of a sliding-leg tripod as an add-on device for manufacturing

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Fengfeng Xi ◽  
Wanzhi Han ◽  
Marcel Verner ◽  
Andrew Ross
Keyword(s):  
Laser Scanning ◽  
System Analysis ◽  
System Modeling ◽  
Kinematic Model ◽  
Joint Space ◽  
Cnc Machine Tools ◽  
System Control ◽  
System Modelling ◽  
Cnc Machine ◽  
Analysis System

This paper presents the work on developing a sliding-leg tripod as a programmable add-on device for manufacturing. The purpose is to enhance the capabilities of any machine by providing it with a more flexible range of motion. This device can be used as a toolhead for CNC machine tools and robots, or as a work stage for coordinate measuring machines and laser scanning systems. In this paper, system modelling, analysis and control of this device is presented. System modeling includes mobility study, kinematic model and inverse kinematics. System analysis includes workspace analysis, transmission ratio and stiffness analysis. System control includes path planning, joint space control and Cartesian space prediction. It is shown that the proposed device can provide flexibility and dexterity to machines.

Coulomb interaction energy including overlap effects for the ground state of RbCs beyond 7 Å

1996 ◽  
Vol 74 (3-4) ◽  
pp. 155-158
Author(s):  
K. Hussein
Keyword(s):  
Interaction Energy ◽  
Coulomb Interaction ◽  
Configuration Space ◽  
Ground State ◽  
Present Method ◽  
Second Order ◽  
Experimental Results ◽  
Coulomb Energy ◽  
First Order ◽  
Dispersion Terms

We use a perturbative model based on a partition of the configuration space into four regions to calculate the Coulomb energy including charge-overlap effects (induction and dispersion terms) for the interaction between two atoms Rb(5s2S) and Cs(6s2S). Results for first-order electrostatic as well as second-order induction and dispersion energies will be presented in the range 13 < R < 25 a.u. The damping functions for the various dispersion terms varying as R−6, R−8, and R−10 in the range of large R have also been determined, and fitted analytical forms will be displayed for these terms. From comparison with accurate experimental results, the present method is seen to be valid for values of R beyond 7 Å (1 Å = 10−10 m).

A New Yaw Dynamic Model for Improved High Speed Control of a Farm Tractor

2002 ◽  
Vol 124 (4) ◽  
pp. 659-667 ◽  
Author(s):  
David M. Bevly ◽  
J. Christian Gerdes ◽  
Bradford W. Parkinson
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Kinematic Model ◽  
Second Order ◽  
Lateral Control ◽  
Relaxation Length ◽  
High Speeds ◽  
Farm Tractor ◽  
Bicycle Model ◽  
Higher Order Models

This paper presents the system identification of a new model for the farm tractor’s yaw dynamics in order to improve automatic control at higher speeds and understand controller limitations from neglecting these dynamics. As speed increases, higher order models are required to maintain accurate lateral control of the vehicle. Neglecting these dynamics can cause the controller to become unstable at the bandwidths required for accurate control at higher speeds. The yaw dynamic model, which is found to be dominated by a second order response, is identified for multiple speeds to determine the effect of velocity on the model. The second order yaw dynamics cannot be represented by the traditional bicycle model. An analytical derivation shows that the model characteristics can, however, be captured by a model consisting of a significant (non-negligible) relaxation length in the front tire. Experimental results are presented showing that the new yaw dynamic model can provide lateral control of the tractor to within 4 cm (1σ) at speeds up to 8 m/s. These results are shown to be an improvement, at high speeds, over controllers based on models (such as a kinematic model) previously used for control of farm equipment.

SECOND-ORDER LAGRANGIAN DYNAMICS IN THE PHASE-SPACE: SOME EXAMPLES

2012 ◽  
Vol 27 (10) ◽  
pp. 1250062
Author(s):  
CONSTANTIN BIZDADEA ◽  
MARIA-MAGDALENA BÂRCAN ◽  
MIHAELA TINCA MIAUTĂ ◽  
SOLANGE-ODILE SALIU
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Finite Number ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Hamiltonian Formulation ◽  
Second Order ◽  
Lagrangian Formulation ◽  
Field Theories ◽  
Lagrangian Dynamics

By means of a class of nondegenerate models with a finite number of degrees of freedom, it is proved that given a Hamiltonian formulation of dynamics, there exists an equivalent second-order Lagrangian formulation whose configuration space coincides with the Hamiltonian phase-space. The above result is extended to scalar field theories in a Lorentz-covariant manner.

Matrix Analysis of Second-Order Kinematic Constraints of Single-Loop Linkages in Screw Coordinates

2018 ◽  
Author(s):  
Liheng Wu ◽  
Andreas Müller ◽  
Jian S. Dai
Keyword(s):  
Quadratic Forms ◽  
Hessian Matrix ◽  
Coefficient Matrix ◽  
Higher Order ◽  
Second Order ◽  
Matrix Analysis ◽  
Kinematic Constraints ◽  
Single Loop ◽  
Order Analysis ◽  
Order Constraints

Higher order loop constraints play a key role in the local mobility, singularity and dynamic analysis of closed loop linkages. Recently, closed forms of higher order kinematic constraints have been achieved with nested Lie product in screw coordinates, and are purely algebraic operations. However, the complexity of expressions makes the higher order analysis complicated and highly reliant on computer implementations. In this paper matrix expressions of first and second-order kinematic constraints, i.e. involving the Jacobian and Hessian matrix, are formulated explicitly for single-loop linkages in terms of screw coordinates. For overconstrained linkages, which possess self-stress, the first- and second-order constraints are reduced to a set of quadratic forms. The test for the order of mobility relies on solutions of higher order constraints. Second-order mobility analysis boils down to testing the property of coefficient matrix of the quadratic forms (i.e. the Hessian) rather than to solving them. Thus, the second-order analysis is simplified.

Rules, Defeasibility, and the Psychology of Exceptions

2020 ◽  
pp. 55-64
Author(s):  
Frederick Schauer
Keyword(s):  
Social Psychology ◽  
International Law ◽  
Experimental Research ◽  
Second Order ◽  
Decision Makers ◽  
First Order ◽  
Order Constraints ◽  
Domestic Law

An important aspect of international law is that it typically lacks the formal, structured, and institutional enforcement and sanctioning mechanisms of domestic law. As a result, decision-makers constrained by international law are often faced with applying the rules of international law to their own action. We know from H.L.A. Hart and others that such internalization is possible, but we know from a great deal of experimental research in cognitive and social psychology that imposing second-order constraints on one’s first-order preferences is difficult and rare without a sanctioning mechanism. As a result, there exists a serious risk that treating the rules of international law as defeasible and subject to exceptions will render the constraints of international law ineffectual when actors are making the decisions about whether and when the exceptions to constraining rules apply to their own actions.

Sign in / Sign up

Export Citation Format

Share Document