Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading

The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.

A Stiffness Variable Passive Compliance Device with Reconfigurable Elastic Inner Skeleton and Origami Shell

Devices with variable stiffness are drawing more and more attention with the growing interests of human-robot interaction, wearable robotics, rehabilitation robotics, etc. In this paper, the authors report on the design, analysis and experiments of a stiffness variable passive compliant device whose structure is a combination of a reconfigurable elastic inner skeleton and an origami shell. The main concept of the reconfigurable skeleton is to have two elastic trapezoid four-bar linkages arranged in orthogonal. The stiffness variation generates from the passive deflection of the elastic limbs and is realized by actively switching the arrangement of the leaf springs and the passive joints in a fast, simple and straightforward manner. The kinetostatics and the compliance of the device are analyzed based on an efficient approach to the large deflection problem of the elastic links. A prototype is fabricated to conduct experiments for the assessment of the proposed concept. The results show that the prototype possesses relatively low stiffness under the compliant status and high stiffness under the stiff status with a status switching speed around 80 ms.

Analysis and Validation of a Flexible Planar Two Degrees-of-Freedom Parallel Manipulator With Structural Passive Compliance

Passive compliance plays an important role in robot pick-and-place manipulation where large interaction force will be produced in response to small misalignments. In this paper, the authors report on compliance analysis and validation of a novel planar pick-and-place parallel manipulator consisting of a flexible limb. In the proposed manipulator, a planar flexible parallelogram linkage, which is coupled with a rigid one, is introduced to connect the moving and the base platforms. Since the flexible parallelogram linkage is capable of producing large deformation in both the horizontal and the vertical directions, the end effector of the manipulator can generate wide-range motions because of the flexible links. An efficient approach to the large deflection problem of flexible links is used to precisely predict the kinetostatics of the manipulator. Then, a compensation algorithm to the structural deflection of the links can be developed to actively control the position of the parallel manipulator’s end effector. The merit of the proposed flexible manipulator is its intrinsic passive compliance while performing pick-and-place tasks. A prototype is fabricated to conduct experiments for the validation of the proposed idea. The results show that the prototype has acceptable positioning accuracy, even when a large external load is exerted on its end effector. The compliance properties of the proposed flexible manipulator have also been verified in both the horizontal and the vertical directions.

Large Deflection of Tip Loaded Beam with Differential Transformation Method

This paper deals with large deflection problem of a cantilever beam with a constant section under the action of a transverse tip load. The differential transformation method (DTM) is used to solve the nonlinear differential equation governing the problem. An approach treats trigonometric nonlinearity is used in DTM. The results obtained from DTM are compared with those results obtained by the finite difference method and they agree well.