Higher-order Taylor approximation of finite motions in mechanisms

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1190-1201 ◽  
Author(s):  
J. J. de Jong ◽  
A. Müller ◽  
J. L. Herder
Keyword(s):  
Screw Theory ◽  
Recursive Algorithm ◽  
Higher Order ◽  
Parallel Mechanisms ◽  
Lie Group Theory ◽  
Loop Closure ◽  
Matrix Operations ◽  
Motion Characteristics ◽  
Derivatives Of ◽  
Insight Into

SUMMARYHigher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.

Type Synthesis of 3-RSR Equivalent 2R1T Parallel Mechanisms

2018 ◽  
Author(s):  
Ziming Chen ◽  
Yanwen Li ◽  
Zhen Huang ◽  
Xianwen Kong
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Motion Patterns ◽  
Continuous Rotations ◽  
Motion Characteristics

Parallel mechanisms (PMs) with two rotational and one translational (2R1T) degrees of freedom (DOFs) have attracted much attention these years. The 2R1T PMs can be divided into various categories due to different motion patterns, such as the UP equivalent PMs, the RPR equivalent PMs, the PU equivalent PMs and the 3-PPS equivalent PMs. In this paper, the 2R1T PMs have the same motion characteristics with the 3-RSR PM are studied and synthesized. This kind of PMs can be called as 3-RSR equivalent 2R1T PMs. The 3-RSR equivalent 2R1T PMs can realize both continuous rotations about fixed axes and continuous translation along fixed directions. The constraint and motion characteristics of the 3-RSR equivalent 2R1T PMs are analyzed. The design of the branches for the 3-RSR equivalent 2R1T PMs is dealt with using the screw theory and the subchains. A group of novel 3-RSR equivalent 2R1T PMs are obtained.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Insight into the Secondary Metabolites of Geum urbanum L. and Geum rivale L. Seeds (Rosaceae)

Plants ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1219
Author(s):  
Marek Bunse ◽  
Peter Lorenz ◽  
Florian C. Stintzing ◽  
Dietmar R. Kammerer
Keyword(s):  
Fatty Acids ◽  
Phenolic Compounds ◽  
Unsaturated Fatty Acids ◽  
Asiatic Acid ◽  
Cosmetic Products ◽  
Nutritional Properties ◽  
First Time ◽  
Derivatives Of ◽  
Geum Urbanum ◽  
Insight Into

The present study aimed at the identification and quantitation of phenolic compounds, fatty acids, and further characteristic substances in the seeds of Geum urbanum L. and Geum rivale L. For this purpose, individual components of extracts recovered with MeOH, CH2Cl2, and by cold-pressing, respectively, were characterized by HPLC-DAD/ESI-MSn and GC/MS and compared with reference compounds. For both Geum species, phenolic compounds, such as flavonoids and gallic acid derivatives, and triterpenes, such as saponins and their aglycones, were detected. Surprisingly, both Geum species revealed the presence of derivatives of the triterpenoid aglycons asiatic acid and madecassic acid, which were characterized for the first time in the genus Geum. Furthermore, the fatty acids of both species were characterized by GC–MS after derivatization. Both species showed a promising fatty-acid profile in terms of nutritional properties because of high proportions of unsaturated fatty acids. Linoleic acid and linolenic acid were most abundant, among other compounds such as palmitic acid and stearic acid. In summary, the present study demonstrates the seeds of G. urbanum and G. rivale to be a valuable source of unsaturated fatty acids and bioactive phenolics, which might be exploited for nutritional and cosmetic products and for phytotherapeutic purposes.

Stacking angle dependent multiple excitonic resonances in bilayer tungsten diselenide

Nanophotonics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 3881-3887
Author(s):  
Ankit Arora ◽  
Pramoda K. Nayak ◽  
Tejendra Dixit ◽  
Kolla Lakshmi Ganapathi ◽  
Ananth Krishnan ◽  
...  
Keyword(s):  
Chemical Vapour ◽  
Optoelectronic Devices ◽  
Interlayer Coupling ◽  
Higher Order ◽  
Doping Effect ◽  
Many Body ◽  
Si Substrate ◽  
Tungsten Diselenide ◽  
Body Dynamics ◽  
Insight Into

AbstractWe report on multiple excitonic resonances in bilayer tungsten diselenide (BL-WSe2) stacked at different angles and demonstrate the use of the stacking angle to control the occurrence of these excitations. BL-WSe2 with different stacking angles were fabricated by stacking chemical vapour deposited monolayers and analysed using photoluminescence measurements in the temperature range 300–100 K. At reduced temperatures, several excitonic features were observed and the occurrences of these exitonic resonances were found to be stacking angle dependent. Our results indicate that by controlling the stacking angle, it is possible to excite or quench higher order excitations to tune the excitonic flux in optoelectronic devices. We attribute the presence/absence of multiple higher order excitons to the strength of interlayer coupling and doping effect from SiO2/Si substrate. Understanding interlayer excitations will help in engineering excitonic devices and give an insight into the physics of many-body dynamics.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

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