Flexible multibody modelling for exact constraint design of compliant mechanisms

Abstract

In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system's degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly.

Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints

“…Engineering experiences suggest that flexibility of bodies, elasticity of bearings, assembly stresses, thermal loads, joint clearances as well as geometric imperfections (in [24], it was shown that, in the case of redundantly constrained mechanisms, the rigid body assumption must be accompanied by a postulate that links are geometrically perfect) should be taken into account, when solving for realistic reactions. In many models, elasticity of bodies is considered, however, some effects associated with constraint redundancy are still observed, even when mechanisms are modeled as entirely flexible systems, e.g., [1,21]. Quite often, in a multibody model, only selected rigid bodies are replaced by their deformable substitutes, e.g., [37], which not always leads to correct results.…”

Development of two degrees of freedom deterministic parallel robotic arm unit

“…Generally, a robotic arm needs to be kinematically determinate and statically determinate to acquire high orientation accuracy [3] during the whole range of operation. Robotic arm system that is not both kinematically and statically determinate will have some disadvantages.…”

“…On one hand, an under-constrained robotic arm system suffers from motion uncertainty. On the other hand, in an overconstrained system natural frequencies and stiffness are sensitive to the small misalignments [3] that inevitable during the assembly of the robotic arm units. Besides, the induced deformations may overload sensitive components of an over constrained robotic system [4].…”

Analyzing Overconstrained Design of Compliant Mechanisms

“…In [9,10] we proposed a flexible multibody modeling approach which is implemented in the SPACAR software package [11]. This flexible multibody approach is based on a non-linear finite element method.…”

“…The next two sections start with a summary of our modeling and analysis approach of overconstrained and underconstrained systems as has been presented earlier [9,10]. Next, the visualization of the overconstrained modes in the system is discussed in more detail.…”