Constraint Wrench Formulation for Closed-Loop Systems Using Two-Level Recursions

In order to compute the constraint moments and forces, together referred here as wrenches, in closed-loop mechanical systems, it is necessary to formulate a dynamics problem in a suitable manner so that the wrenches can be computed efficiently. A new constraint wrench formulation for closed-loop systems is presented in this paper using two-level recursions, namely, subsystem level and body level. A subsystem is referred here as the serial- or tree-type branches of a spanning tree obtained by cutting the appropriate joints of the closed loops of the system at hand. For each subsystem, unconstrained Newton–Euler equations of motion are systematically reduced to a minimal set in terms of the Lagrange multipliers representing the constraint wrenches at the cut joints and the driving torques/forces provided by the actuators. The set of unknown Lagrange multipliers and the driving torques/forces associated to all subsystems are solved in a recursive fashion using the concepts of a determinate subsystem. Next, the constraint forces and moments at the uncut joints of each subsystem are calculated recursively from one body to another. Effectiveness of the proposed algorithm is illustrated using a multiloop planar carpet scraping machine and the spatial RSSR (where R and S stand for revolute and spherical, respectively) mechanism.

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Efficient Parallel Computer Simulation of the Motion Behaviors of Closed-Loop Multibody Systems

Volume 10: Mechanics of Solids and Structures, Parts A and B ◽

10.1115/imece2007-41912 ◽

2007 ◽

Author(s):

Shanzhong Duan ◽

Andrew Ries

Keyword(s):

Parallel Computing ◽

Multibody Systems ◽

Closed Loop ◽

High Efficiency ◽

Equations Of Motion ◽

Parallel Computer ◽

Constraint Forces ◽

Computing Systems ◽

Closed Loops

This paper presents an efficient parallelizable algorithm for the computer-aided simulation and numerical analysis of motion behaviors of multibody systems with closed-loops. The method is based on cutting certain user-defined system interbody joints so that a system of independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) method. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. For multibody systems with closed-loops, joint separations play both a role of creation of parallelism for computing load distribution and a role of opening a closed-loop for use of the O(n) algorithm. Joint separation strategies provide the flexibility for use of the algorithm so that it can easily accommodate the available number of processors while maintaining high efficiency. The algorithm gives the best performance for the application scenarios for n>>1 and n>>m, where n and m are number of degree of freedom and number of constraints of a multibody system with closed-loops respectively. The algorithm can be applied to both distributed-memory parallel computing systems and shared-memory parallel computing systems.

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Symbolic Linearized Equations for Nonholonomic Multibody Systems With Closed-Loop Kinematics

Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2018-85823 ◽

2018 ◽

Cited By ~ 1

Author(s):

Márton Kuslits ◽

Dieter Bestle

Keyword(s):

Lagrange Multipliers ◽

Multibody Systems ◽

Closed Loop ◽

Equations Of Motion ◽

Linear Equations ◽

Algebraic Equations ◽

Computationally Efficient ◽

Linearized Equations ◽

Nonlinear Equations Of Motion ◽

Loop Constraints

Multibody systems and associated equations of motion may be distinguished in many ways: holonomic and nonholonomic, linear and nonlinear, tree-structured and closed-loop kinematics, symbolic and numeric equations of motion. The present paper deals with a symbolic derivation of nonlinear equations of motion for nonholonomic multibody systems with closed-loop kinematics, where any generalized coordinates and velocities may be used for describing their kinematics. Loop constraints are taken into account by algebraic equations and Lagrange multipliers. The paper then focuses on the derivation of the corresponding linear equations of motion by eliminating the Lagrange multipliers and applying a computationally efficient symbolic linearization procedure. As demonstration example, a vehicle model with differential steering is used where validity of the approach is shown by comparing the behavior of the linearized equations with their nonlinear counterpart via simulations.

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A Computational Method for the Dynamic Analysis of Planar Linkages With Applications

Volume 2A: 27th Design Automation Conference ◽

10.1115/detc2001/dac-21020 ◽

2001 ◽

Author(s):

Hazem A. Attia

Keyword(s):

Closed Loop ◽

Equations Of Motion ◽

Open Loop ◽

Rigid Bodies ◽

Transformation Matrix ◽

Computational Method ◽

Constraint Forces ◽

Constrained System ◽

Velocity Transformation ◽

Planar Linkages

Abstract This paper presents a computational method for generating the equations of motion of planar linkages consisting of interconnected rigid bodies. The formulation uses initially the rectangular Cartesian coordinates of an equivalent constrained system of particles to define the configuration of the mechanism. This results in a simple and straightforward procedure for generating the equations of motion. The equations of motion are then derived in terms of relative joint variables through the use of a velocity transformation matrix. The velocity transformation matrix relates the relative joint velocities to the Cartesian velocities. For the open loop case, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For the closed loop case, suitable joints should be cut and few cut-joints constraint equations should be included for each closed loop. Examples are used to demonstrate the generality and efficiency of the proposed method.

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Neural Computation in Embodied Closed-Loop Systems for the Generation of Complex Behavior: From Biology to Technology

10.3389/978-2-88945-605-5 ◽

2018 ◽

Keyword(s):

Closed Loop ◽

Neural Computation ◽

Complex Behavior ◽

Closed Loop Systems

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METHOD OF SYNTHESIS OF CLOSED-LOOP SYSTEMS OF ACTIVE SHIELDING MAGNETIC FIELD OF POWER TRANSMISSION LINES

Tekhnichna Elektrodynamika ◽

10.15407/techned2016.04.008 ◽

2016 ◽

Vol 2016 (4) ◽

pp. 8-10 ◽

Cited By ~ 1

Author(s):

B.I. Kuznetsov ◽

◽

A.N. Turenko ◽

T.B. Nikitina ◽

A.V. Voloshko ◽

...

Keyword(s):

Magnetic Field ◽

Transmission Lines ◽

Closed Loop ◽

Power Transmission ◽

Power Transmission Lines ◽

Closed Loop Systems ◽

Active Shielding

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102-LB: Cross-Study Comparisons Done Right: An Illustration Using Two Pivotal Trials of Closed-Loop Systems

Diabetes ◽

10.2337/db20-102-lb ◽

2020 ◽

Vol 69 (Supplement 1) ◽

pp. 102-LB

Author(s):

MARC D. BRETON ◽

ROY BECK ◽

RICHARD M. BERGENSTAL ◽

BORIS KOVATCHEV

Keyword(s):

Closed Loop ◽

Closed Loop Systems

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Time in range for multiple technologies in type 1 diabetes: a systematic review and network meta-analysis

10.2337/figshare.12116691 ◽

2020 ◽

Author(s):

Anthony Pease ◽

Clement Lo ◽

Arul Earnest ◽

Velislava Kiriakova ◽

Danny Liew ◽

...

Keyword(s):

Systematic Review ◽

Type 1 Diabetes ◽

Closed Loop ◽

Meta Analysis ◽

Management Strategies ◽

Glucose Testing ◽

Closed Loop Systems ◽

Percent Time ◽

Time In Range

Background: Time-in-range is a key glycaemic metric, and comparisons of management technologies for this outcome are critical to guide device selection. Purpose: We conducted a systematic review and network meta-analysis to compare and rank technologies for time in glycaemic ranges. Data sources: We searched All Evidenced Based Medicine Reviews, CINAHL, EMBASE, MEDLINE, MEDLINE In-Process and other non-indexed citations, PROSPERO, PsycINFO, PubMed, and Web of Science until 24 April, 2019. Study selection: We included randomised controlled trials >2 weeks duration comparing technologies for management of type 1 diabetes in adults (>18 years of age), excluding pregnant women. Data extraction: Data were extracted using a predefined template. Outcomes were percent time with sensor glucose levels 3.9–10.0mmol/l (70–180mg/dL), >10.0mmol/L (180mg/dL), and <3.9mmol/L (70mg/dL). Data synthesis: We identified 16,772 publications, of which 14 eligible studies compared eight technologies comprising 1,043 participants. Closed loop systems lead to greater percent time-in-range than any other management strategy and was 17.85 (95% predictive interval [PrI] 7.56–28.14) higher than usual care of multiple daily injections with capillary glucose testing. Closed loop systems ranked best for percent time-in-range or above range utilising surface under the cumulative ranking curve (SUCRA–98.5 and 93.5 respectively). Closed loop systems also ranked highly for time below range (SUCRA–62.2). Limitations: Overall risk of bias ratings were moderate for all outcomes. Certainty of evidence was very low. Conclusions: In the first integrated comparison of multiple management strategies considering time-in-range, we found that the efficacy of closed loop systems appeared better than all other approaches.

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