Abstract
Hybrid rigid–flexible mechanisms are a type of compliant mechanism that combines rigid and flexible elements, being that their mobility is due to rigid-body joints and the relative flexibility of bendable rods. Two of the modeling methods of flexible rods are the Cosserat rod model and its simplification, the Kirchhoff rod model. Both of them present a system of differential equations that must be solved in conjunction with the boundary constraints of the rod, leading to a boundary value problem (BVP). In this work, two methods to solve this BVP are applied to analyze the influence of external loads in the movement of hybrid compliant mechanisms. First, a shooting method (SM) is used to integrate directly the shape of the flexible rod and the forces that appear in it. Then, an integration with elliptic integrals (EI) is carried out to solve the workspace of the compliant element, considering its buckling mode. Applying both methods, an algorithm that obtains the locus of all possible trajectories of the mechanism’s coupler point, and detects the buckling mode change, is developed. This algorithm also allows calculating all possible circuits of the mechanism. Thus, the performance of this method within the path analysis of mechanisms is demonstrated.
Highlights
A compliant body is one whose motion depends on its geometry, its material properties and the location and magnitude of the applied forces
If a body of this kind belongs to a mechanism, it is known as a compliant element
When a mechanism is fully composed of compliant elements, e.g., slender rods, it is named a compliant mechanism, and it gains all or part of its mobility, thanks to the relative flexibility of those compliant elements
Summary
A compliant body is one whose motion depends on its geometry, its material properties and the location and magnitude of the applied forces. It should be noted that, in the case of compliant mechanisms, it is not needed to disassemble any link to obtain the different circuits but to deform a flexible rod through an external load. Another model is the Cosserat rod model, which produces the equations that describe the deformed shape of a slender flexible element and the loads that appear in it [13,14] This modeling method leads to a set of differential equations that, in conjunction with the boundary constraints of the compliant element, takes the form of a boundary value problem (BVP). The framework needed to describe the shape of a slender rod in space includes three main aspects that, coupled, generate the nonlinear system of differential equations that has to be solved in order to obtain the relationship between force and deformation. These are as follows: a kinematic definition of the deformed rod, material constitutive laws and static equilibrium equations
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