• 한국운동역학회지
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• 제27권2호
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• pp.109-116
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• 2017

Objective: This study aimed to investigate the relationship between leg stiffness and kinematic variables according to load while running. Method: Participants included eight healthy men (mean age, $22.75{\pm}1.16years$; mean height: $1.73{\pm}0.01m$; mean body weight, $71.37{\pm}5.50kg$) who ran with no load or a backpack loaded with 14.08% or 28.17% of their body weight. The analyzed variables included leg stiffness, ground contact time, center of gravity (COG) displacement and Y-axis velocity, lower-extremity joint angle (hip, knee, ankle), peak vertical force (PVF), and change in stance phase leg length. Results: Dimensionless leg stiffness increased significantly with increasing load during running, which was the result of increased PVF and contact time due to decreased leg lengths and COG displacement and velocity. Leg length and leg stiffness showed a negative correlation (r = -.902, $R^2=0.814$). COG velocity showed a similar correlation with COG displacement (r = .408, $R^2=.166$) and contact time (r = -.455, $R^2=.207$). Conclusion: Dimensionless leg stiffness increased during running with a load. In this investigation, leg stiffness due to load increased was most closely related to the PVF, knee joint angle, and change in stance phase leg length. However, leg stiffness was unaffected by change in contact time, COG velocity, and COG displacement.

• 대한기계학회논문집
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• 제18권10호
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• pp.2640-2652
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• 1994

The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.

• 한국전기전자재료학회논문지
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• 제18권6호
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• pp.521-526
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• 2005

Within wafer non-uniformity(WIWNU) improves as the stiffness of pad decrease. We designed the pad groove to study of pad stiffness on WIWNU in Chemical mechanical polishing(CMP) and measured the pad stiffness according to groove width. The groove influences effective pad stiffness although original mechanical properties of pad are unchanged by grooving. Also, it affects the flow of slurry that has an effect on the lubrication regime and polishing results. An Increase of the apparent contact area of pad by groove width results in decrease of effective pad stiffness. WIWNU and profile of removal tate improved as effective pad stiffness decreased. Because grooving the pad reduce its effective stiffness and it makes slurry distribution to be uniform. Futhermore, it ensures that pad conforms to wafer-scale flatness variability. By grooving the top pad, it is possible to reduce its stiffness and hence reduce WIWNU and edge effect.

• Geomechanics and Engineering
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• 제1권2호
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• 한국기계가공학회지
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• 제16권5호
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• pp.19-24
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• 2017

In this research, a practical stiffness calculation method is developed and applied for modifying the height of the headstock, turret, and tailstock of a CNC lathe to enlarge the turntable diameter. The casting structure is assumed to be a rigid body and the linear motion element to be an elastic spring to simplify the turret stiffness calculation model. The stiffness of the sliding guide and ball screw of the original lathe is measured with a push tester and LVDT sensor, and the turret stiffness of the modified lathe is predicted and compared with experimental results to verify the model. The measured stiffness of the original turret is $0.17kN/{\mu}m$ and that of the modified turret is $0.11kN/{\mu}m$, i.e., an 18% difference from the predicted result. The verified stiffness calculation model can be used to develop another modified lathe.

• Smart Structures and Systems
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• 제9권2호
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• pp.189-206
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• 2012

This paper focuses on the actuation system combined with a piezoelectric transducer and an electric circuit, which leads to a new insight; the electric actuation system is equivalent to mechanical variable-stiffness actuation systems. By controlling the switch in the circuit, the electric status of the piezoelectric transducer is changed, and consequently a variable-stiffness mechanism is achieved on the electric actuator. This proposed actuator features a shift in the equilibrium point of force, while conventional electrically-induced variable-stiffness actuators feature the variation of the stiffness value. We intensively focus on the equilibrium shift in the actuation system, which has been neglected. The stiffness of the variable-stiffness actuator is periodically modulated by controlling the switch, to suppress the vibration of the system in an open-loop way. It is proved that this electric actuator is equivalent to its mechanical counterpart, and that the electrical version has some practical advantages over the mechanical one. Furthermore, another kind of electrically-induced variable-stiffness actuator, using an energy-recycling mechanism is also discussed from the viewpoint of open-loop vibration control. Extensive numerical simulations provide comprehensive assessment on both electrically-induced variable-stiffness actuators employed for open-loop vibration control.

• International Journal of Naval Architecture and Ocean Engineering
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• 제4권3호
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• pp.313-321
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• 2012

Vibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis.

• 대한의용생체공학회:의공학회지
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• 제32권2호
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• pp.105-108
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• 2011

The purpose of the present study was to analyze the lower stiffness over the difference between soft and stiff landings during hopping. Five male subjects performed hopping on two legs at 2.5 Hz. During the experiments, 3D motion capture system was used to obtain the kinematic data and two force plates were synchronized to calculate the kinetic data. We determined lower extremity stiffness of the knee and ankle from kinetic and kinematic data. Leg stiffness was approximately 1.2-times significantly higher in stiff landing than in soft landing_ There was no significant difference in knee joint stiffness between soft and stiff landings. Ankle joint stiffness was approximately 1.34-times significantly higher in stiff landing than in soft landing. These results suggest that humans adjust lower extremity stiffness over the comparison of two different landing methods we evaluated.

• 한국정밀공학회지
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• 제29권7호
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• pp.723-729
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• 2012

Spring-like leg models have been employed to explain various dynamic characteristics in human walking. However, this leg stiffness model has limitations to represent complex motion of actual human gait, especially the behaviors of each lower limb joint. The purpose of this research was to determine changes of total leg stiffness and lower limb joint stiffness with gait speed in knee osteoarthritis. Joint stiffness defined as the ratio of the joint torque change to the angular displacement change. Eight subjects with knee osteoarthritis participated to this study. The subject walked on a 12 m long and 1 m wide walkway with three sets of four different randomly ordered gait speeds, ranging from their self-selected speed to maximum speed. Kinetic and kinematic data were measured using three force plates and an optical marker system, respectively. Joint torques of lower limb joints calculated by a multi-segment inverse dynamics model. Total leg and each lower limb joint had constant stiffness during single support phase. The leg and hip joint stiffness increased with gait speed. The correlation between knee joint angles and torques had significant changed by the degree of severity of knee osteoarthritis.

• Smart Structures and Systems
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• 제24권3호
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• pp.361-377
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• 2019

The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.