Effect of Secondary Motion on Hydrodynamics of a Cylinder Oscillating in Still Fluid

In this study, we conducted numerical simulations to compute the hydrodynamic forces acting on a circular cylinder undergoing bidirectional oscillations in still fluid. The simulations correspond to the regime of attached laminar two-dimensional flow at low values of the Keulegan-Carpenter number (KC ≤ 5) and Reynolds numbers from 35 to 1000 based on the primary motion of the cylinder. The effect of a secondary motion transverse to the primary motion having twice the frequency and a fifth of the amplitude of the latter is investigated and the results are compared with the corresponding case of unidirectional motion and theoretical predictions from Stokes–Wang theory. The results for unidirectional motion show that the computed force in-line with the motion agree well with theory for KC < 1 and KCRe > 100. The agreement between computations and theory improves as KC decreases and Re increases. The addition of a secondary motion with different phase angles with respect to the primary motion did not have any observable effect on the force acting along the direction of the primary motion compared to that for the same unidirectional motion, although it had a marked effect on the distribution of vorticity around the cylinder. The forces on the cylinder undergoing bidirectional oscillations could be well predicted from Stokes–Wang theory applied in each individual direction for the range of parameters examined in this study. The present study provides insight into the relationship between the generation of vorticity around an oscillating cylinder and the fluid forces acting on it.

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

Symmetry is very necessary in flexure mechanisms, which can eliminate parasitic motions, avoid buckling, and minimize thermal and manufacturing sensitivity. This paper proposes two symmetric and compact flexure designs, in-plane 3-DOC (degree of constraint) mechanisms, which are composed of 4 and 6 identical wire beams, respectively. Compared to traditional leaf-beam-based designs, the two present designs have lower stiffness in the primary motion directions, and have smaller stiffness reduction in the parasitic directions. Analytical modelling is conducted to derive the symbolic compliance equations, enabling quick analysis and comparisons of compliances of the two mechanisms. A prototype has been tested statically to compare with analytical models.

Determinate Design and Analytical Analysis of a Class of Symmetrical Flexure Guiding Mechanisms for Linear Actuators

This paper designs and analyses a class of single-axis translational flexure guiding mechanisms for linear actuators. The proposed flexure mechanisms have symmetrical configurations to eliminate parasitic motion for better precision and can provide large stiffness in the constraint directions and low stiffness in the actuation direction. Each flexure linear mechanism is composed of identical wire beams uniformly distributed in two planes (perpendicular to the actuation direction) with the minimal number of over-constraints. Analytical (symbolic) models are derived to quickly reflect effects of different parameters on performance characteristics of the flexure mechanism, enabling dimensional synthesis of different types of mechanisms. An optimal, compact, and symmetrical, flexure linear mechanism design is finally presented and prototyped with focused discussions on its primary motion.

On the comprehensive static characteristic analysis of a translational bistable mechanism

Bistable mechanisms have two stable positions and their characteristic analysis is much harder than the traditional spring system due to their postbuckling behaviour. As the strong nonlinearity induced by the postbuckling, it is difficult to establish a correct model to reveal the comprehensive nonlinear characteristics. This paper deals with the in-plane comprehensive static analysis of a translational bistable mechanism using nonlinear finite element analysis. The bistable mechanism consists of a pair of fixed-clamped inclined beams in symmetrical arrangement, which is a monolithic design and works within the elastic deformation domain. The displacement-controlled finite element analysis method using Strand7 is first discussed. Then the force–displacement relation of the bistable mechanism along the primary motion direction is described followed by the detailed primary translational analysis for different parameters. A simple analytical (empirical) equation for estimating the negative stiffness is obtained, and experimental testing is performed for a case study. It is concluded that (a) the negative stiffness magnitude has no influence from the inclined angle, but is proportional to the product of the Young’s modulus, beam depth, and cubic ratio for in-plane thickness to the beam length; (b) the unstable position is proportional to the product of the beam length and the Sine function of the inclined angle, and is not affected by the in-plane thickness and the material (or the out-of-plane thickness). The in-plane off-axis (translational and rotational) stiffness is further analysed to show the stiffness changes over the primary motion and the off-axis motion, and a negative rotational stiffness domain has been obtained.

Extended Static Modeling and Analysis of Compliant Compound Parallelogram Mechanisms Considering the Initial Internal Axial Force*

Extended nonlinear analytical modeling and analysis of compound parallelogram mechanisms are conducted in this paper to consider the effect of the initial internal axial force. The nonlinear analytical model of a compound basic parallelogram mechanism (CBPM) is first derived incorporating the initial internal axial force. The stiffness equations of compound multibeam parallelogram mechanisms (CMPMs) are then followed. The analytical maximal stress under the primary actuation force only is also derived to determine the maximal primary motion (motion range). The influence of initial internal axial forces on the primary motion/stiffness is further quantitatively analyzed by considering different slenderness ratios, which can be employed to consider active displacement preloading control and/or thermal effects. The criterion that the primary stiffness may be considered “constant” is defined and the initial internal axial force driven by a temperature change is also formulated. A physical preloading system to control the initial internal axial force is presented and testing results of the object CBPM are compared with theoretical ones.

Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

This paper deals with nonlinear analytical models of a class of compound multibeam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. First, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.

Extended Nonlinear Analysis of Exactly-Constrained Compliant Compound Parallelogram Mechanisms

Extended nonlinear analysis of compliant compound parallelogram mechanisms is conducted in this paper. The analytical nonlinear model of a compound basic parallelogram mechanism (CBPM) is first derived incorporating the initial internal axial force. The stiffness equations of compound multi-beam parallelogram mechanisms (CMPMs) are then followed. The effect of initial internal axial forces on the primary motion is further analyzed, which can be employed to consider active displacement preloading control and thermal effects etc. It is shown that negative initial internal axial force will reduce the primary stiffness, and vice versa. The criteria for which the primary stiffness may be considered “constant” is defined and the initial internal axial force driven by temperature change is also formulated. The dynamic analysis of a CMPM using nonlinear finite element analysis (FEA) is finally carried out to show the modal frequency and the forced excitation response in the primary motion direction.

On the infinitely-stable rotational mechanism using the off-axis rotation of a bistable translational mechanism

Different from the prior art concentrating on the primary translation of bistable translational mechanisms this paper investigates the off-axis rotation behaviour of a bistable translational mechanism through displacing the guided primary translation at different positions. Moment-rotation curves obtained using the nonlinear finite element analysis (FEA) for a case study show the multiple stable positions of the rotation under each specific primary motion, suggesting that an infinitely-stable rotational mechanism can be achieved by controlling the primary motion. In addition, several critical transition points have been identified and qualitative testing has been conducted for the case study.