Abstract
This article deals with the development of a simple model to evaluate the first natural frequencies of over-constrained parallel kinematic machines (PKMs). The simplest elasto-dynamic models are based on multi-body approaches. However, these approaches require an expression of the Jacobian matrices that may be difficult to obtain for complex PKMs. Therefore, this paper focuses on the determination of the global mass and stiffness matrices of an over-constrained PKM in stationary configurations without the use of Jacobian matrices. The PKM legs are modeled by beams. Because the legs are connected to a moving platform and the mechanism is over-constrained, constraint equations between the parameters that model the deformation of each leg are determined according to screw theory. The first natural frequencies and associated modes can then be determined. It should be noted that the proposed method can be easily used at the conceptual design stage of PKMs. The Tripteor X7 machine is used as an illustrative example and is characterized experimentally.
Highlights
Parallel Kinematic Robots are used in many fields such as medicinal, aerospace, rehabilitation, and astronomy [1]
An over-constrained Parallel Kinematic Machine Tools (PKMs) is defined as a PKM with common or redundant constraints that can be removed without changing the kinematic properties of the mechanism [9]
It is of prime importance to express a parameterized elasto-dynamic model for over-constrained PKMs
Summary
Parallel Kinematic Robots are used in many fields such as medicinal, aerospace, rehabilitation, and astronomy [1]. A few Parallel Kinematic Machine Tools (PKMs) are used in the automotive or aeronautical industries for High-Speed Machining (HSM) operations [3]. Their dynamic performances, in terms of acceleration, are better for an equivalent motorization than Serial Kinematic Machine Tools (SKMs) due their closed-loop architecture [4]. Depending on the machined part position, marks appear on the machined surfaces To minimize these vibrations, it is of prime importance to express a parameterized elasto-dynamic model for over-constrained PKMs. To minimize these vibrations, it is of prime importance to express a parameterized elasto-dynamic model for over-constrained PKMs Such a model enables the prediction of static and vibration behavior during the conceptual design stage. It is usually used for validation purposes at the final design stage since it is time-consuming [12–15]
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