Synthesis of RCCC Linkages to Visit Four Given Poses

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Shaoping Bai ◽  
Jorge Angeles
Keyword(s):  
Rigid Body ◽  
Exact Solutions ◽  
Kinematic Pair ◽  
Approximate Nature ◽  
The Asymmetry ◽  
Robust Formulation

This paper focuses on the problem of synthesis of spatial four-bar linkages of the RCCC type for rigid-body guidance with four given poses, R denoting a revolute, C a cylindrical kinematic pair. While synthesis equations for CC and RC dyads are available in the literature, the synthesis of spatial RCCC four-bar linkages requires special attention, due to its asymmetric topology. We revisit the problem to cope robustly with the asymmetry, namely, the approximate nature of the RC dyad and the infinity of exact solutions of the CC dyad for the number of given poses. Our approach includes a robust formulation of the synthesis of CC dyads, for the determination of axis-congruences. Moreover, we formulate a uniform synthesis equation, which enables us to treat both RC and CC dyads, with properly selected constraints for both cases. Two design examples are included.

On the direct problem singularities of a class of 3-DOF parallel manipulators

Robotica ◽  
2004 ◽  
Vol 22 (4) ◽  
pp. 389-394 ◽  
Author(s):  
R. Di Gregorio
Keyword(s):  
Rigid Body ◽  
Direct Problem ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Pair ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Direct Kinematics ◽  
Relative Motions

The 3-PS structure features one rigid body (platform) connected to another rigid body (base) by means of three kinematic chains (limbs) of type PS (P and S stand for prismatic pair and spherical pair, respectively). All the 3-degree-of-freedom parallel manipulators with three connectivity-5 limbs, each one constituted of one passive (i.e. not actuated) prismatic pair, one passive spherical pair and one actuated kinematic pair of any type, become 3-PS structures when the actuated pairs are locked. Direct kinematics of this class of manipulators is tied to the properties of the 3-PS structure. In particular, the direct position analysis is tied to the assembly modes of the 3-PS structure; whereas the determination of the singularities of the direct instantaneous problem is tied to the determination of the singular geometries of the 3-PS structure, where instantaneous relative motions between platform and base are possible. The solution of these two problems is necessary both for designing the manipulators and for controlling them during motion. This paper deal with the determination of the singular geometries of the 3-PS structure.

Determination of viscosity parameters in rigid body-soil interaction

2016 ◽  
pp. 163-165
Author(s):  
G. X. Xojimetov ◽  
D. A. Bekmirzaev ◽  
A. S. Yuvmitov
Keyword(s):  
Rigid Body

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Experimental Determination of Steady and Unsteady Loads on a Surface Piercing, Ventilated Hydrofoil

1969 ◽  
Vol 13 (01) ◽  
pp. 1-11
Author(s):  
G. E. Ransleben
Keyword(s):  
Rigid Body ◽  
Experimental Determination ◽  
Cross Section ◽  
Angle Of Attack ◽  
Chord Length ◽  
Body Rolling

Measured steady and unsteady section lift and moment coefficients at two spanwise locations on a surface-piercing ventilated hydrofoil are presented. The foil, of wedge cross section, was supported vertically, and submerged one chord length from the tip. Excitation in rigid-body rolling and pitching modes to the cantilevered foil produced the unsteady loads. All tests were made at a nominal angle of attack of 12 deg.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

scholarly journals Determination of thermal diffusivity for rigid body at non-stationary thermal conditions

2019 ◽  
Vol 288 ◽  
pp. 012097
Author(s):  
Denis Karpov ◽  
Vladimir Agafonov ◽  
Viktor Pisarenko ◽  
Pavel Berezin ◽  
Oleg Derevianko ◽  
...  
Keyword(s):  
Thermal Diffusivity ◽  
Rigid Body ◽  
Thermal Conditions

Determination of the Limit Cycle by He’s Parameter-Expansion for Oscillators in a u3 / (1 + u2) Potential

2007 ◽  
Vol 62 (7-8) ◽  
pp. 396-398 ◽  
Author(s):  
Li-Na Zhang ◽  
Lan Xu
Keyword(s):  
Exact Solutions ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Expansion Method ◽  
Nonlinear Oscillators ◽  
Mathematical Tool ◽  
Parameter Expansion ◽  
Parameter Expansion Method ◽  
Powerful Mathematical Tool

This paper applies He’s parameter-expansion method to determine the limit cycle of oscillators in a u3/(1+u2) potential. The results are compared with the exact solutions. This shows that the method is a convenient and powerful mathematical tool for the search of limit cycles of nonlinear oscillators.

Off-Resonance Nutation NQR Spectroscopy of Powders

1995 ◽  
Vol 50 (10) ◽  
pp. 957-960 ◽  
Author(s):  
N.Ja. Sinjavsky
Keyword(s):  
The Asymmetry

Abstract The peculiarities of nutation NQR spectra of nuclei with spin I=3/2 in powders are considered in the case of a resonance offset. An equation, which takes into account the offset is given for the determination of the asymmetry η. It is shown that structural of monocrystals by means of nutation spectroscopy are possible.

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