Kinematic modeling and optimal design of a partially compliant four-bar linkage using elliptic integral solution

The nonlinear structural acoustic problem considered in this study is the nonlinear natural frequency analysis of flexible double panels using the elliptic integral solution method. There are very limited studies for this nonlinear structural-acoustic problem, although many nonlinear plate or linear double panel problems have been tackled and solved. A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. One is the von Karman’s plate equation and the other is the homogeneous wave equation. The results obtained from the proposed method approach are verified with those from a numerical method. The effects of vibration amplitude, gap width, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth on the resonant frequencies of the in-phase and out of phase modes are examined.

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Predicting Nonlinear Stiffness, Motion Range, and Load-Bearing Capability of Leaf-Type Isosceles-Trapezoidal Flexural Pivot Using Comprehensive Elliptic Integral Solution

Mathematical Problems in Engineering ◽

10.1155/2020/1390692 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Aimei Zhang ◽

Yanjie Gou ◽

Xihui Yang

Keyword(s):

Elliptic Integral ◽

Integral Solution ◽

Leaf Spring ◽

Nonlinear Stiffness ◽

Load Bearing ◽

Large Rotation ◽

Leaf Type ◽

Proposed Model ◽

Motion Range ◽

Stiffness Characteristics

A leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two leaf springs that are situated in the same plane and intersect at a virtual center of motion outside the pivot. The LITF pivot offers many advantages, including large rotation range and monolithic structure. Each leaf spring of a LITF pivot subject to end loads is deflected into an S-shaped configuration carrying one or two inflection points, which is quite difficult to model. The kinetostatic characteristics of the LITF pivot are precisely modeled using the comprehensive elliptic integral solution for the large-deflection problem derived in our previous work, and the strength-checking method is further presented. Two cases are employed to verify the accuracy of the model. The deflected shapes and nonlinear stiffness characteristics within the range of the yield strength are discussed. The load-bearing capability and motion range of the pivot are proposed. The nonlinear finite element results validate the effectiveness and accuracy of the proposed model for LITF pivots.

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Kinematics modeling of a two DOFs continuum manipulator with uniform notches

MATEC Web of Conferences ◽

10.1051/matecconf/202030905006 ◽

2020 ◽

Vol 309 ◽

pp. 05006

Author(s):

Xiaolong Wang ◽

Haodong Wang ◽

Zhijiang Du ◽

Wenlong Yang

Keyword(s):

Friction Coefficient ◽

Degrees Of Freedom ◽

Elliptic Integral ◽

Load Capacity ◽

Kinematic Model ◽

Kinematic Modeling ◽

Flexible Beams ◽

Kinematics Modeling ◽

Single Port Laparoscopy ◽

Continuum Manipulator

Continuum manipulators have been widely adopted for single-port laparoscopy (SPL). A novel continuum manipulator with uniform notches which has two degrees of freedom (DOFs) is presented in this paper. The arrangement of flexible beams makes it own a higher load capacity. Its kinematic model is coupled with the mechanical model. The comprehensive elliptic integral solution (CEIS) is more practical in the actual deformation of the flexible beams. Based on that method, kinematics modeling is established from the driven space to the Cartesian space. The friction coefficient is an important factor which can affect the kinematic modeling. Therefore, an experimental platform is established to obtain the friction coefficient. The kinematic modeling is verified through the prototype. Experimental results show that the model has high precision.

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