A Substructure Condensed Approach for Kinetostatic Modeling of Compliant Mechanisms with Complex Topology.

Compliant mechanisms with complex topology have previously been employed in various precision devices due to the superiorities of high precision and compact size. In this paper, a substructure condensed approach for kinetostatic analysis of complex compliant mechanisms is proposed to provide concise solutions. In detail, the explicit relationships between the theoretical stiffness matrix, element stiffness matrix, and element transfer matrix for the common flexible beam element are first derived based on the energy conservation law. The transfer matrices for three types of serial-parallel substructures are then developed by combining the equilibrium equations of nodal forces with the transfer matrix approach, so that each branch chain can be condensed into an equivalent beam element. Based on the derived three types of transfer matrices, a kinetostatic model describing only the force-displacement relationship of the input/output nodes is established. Finally, two typical precision positioning platforms with complex topology are employed to demonstrate the conciseness and efficiency of this modeling approach. The superiority of this modeling approach is that the input/output stiffness, coupling stiffness, and input/output displacement relations of compliant mechanisms with multiple actuation forces and complex substructures can be simultaneously obtained in concise and explicit matrix forms, which is distinct from the traditional compliance matrix approach.

Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms.

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

Experimental Study of the Effect of Internal Defects on Stress Waves during Automated Fiber Placement.

The detection technique of component defects is currently only realized to detect offline defects and online surface defects during automated fiber placement (AFP). The characteristics of stress waves can be effectively applied to identify and detect internal defects in material structure. However, the correlation mechanism between stress waves and internal defects remains unclear during the AFP process. This paper proposes a novel experimental method to test stress waves, where continuous loading induced by process itself is used as an excitation source without other external excitation. Twenty-seven groups of thermosetting prepreg laminates under different processing parameters are manufactured to obtain different void content. In order to quantitatively estimate the void content in the prepreg structure, the relation model between the void content and ultrasonic attenuation coefficient is revealed using an A-scan ultrasonic flaw detector and photographic methods by optical microscope. Furthermore, the high-frequency noises of stress waves are removed using Haar wavelet transform. The peaks, the Manhattan distance and mean stress during the laying process are analyzed and evaluated. Partial conclusions in this paper could provide theoretical support for online real-time detection of internal defects based on stress wave characteristics.