On the advantages of instantaneous invariants and geometric kinematics

Roth, Bernard

doi:10.1016/j.mechmachtheory.2014.10.009

Cited by 22 publications

(4 citation statements)

References 10 publications

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“…Instantaneous invariants, mainly the geometric ones, are essential to set problems of kinematic synthesis in analytical form [68][69][70][71][72][73].…”

Section: Analytical Deduction Of Instantaneous Invariants For Complia...mentioning

confidence: 99%

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Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

Iandiorio

Salvini

2023

Micromachines

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The kinematic synthesis of compliant mechanisms based on flexure hinges is not an easy task. A commonly used method is the equivalent rigid model, which involves replacing the flexure hinges with rigid bars connected with lumped hinges using the already known methods of synthesis. This way, albeit simpler, hides some interesting issues. This paper addresses the elasto-kinematics and instantaneous invariants of flexure hinges with a direct approach, making use of a nonlinear model to predict their behaviour. The differential equations that govern the nonlinear geometric response are given in a comprehensive form and are solved for flexure hinges with constant sections. The solution to the nonlinear model is then used to obtain an analytical description of two instantaneous invariants: the centre of instantaneous rotation (c.i.r.) and the inflection circle. The main result is that the c.i.r. evolution, namely the fixed polode, is not conservative but is loading-path dependent. Consequently, all other instantaneous invariants are loading-path dependent, and the property of instantaneous geometric invariants (independent of the motion time law) can no longer be used. This result is analytically and numerically evidenced. In other words, it is shown that a careful kinematic synthesis of compliant mechanisms cannot be addressed by only considering the kinematics as rigid mechanisms, and it is essential to take into consideration the applied loads and their histories.

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“…Instantaneous invariants, mainly the geometric ones, are essential to set problems of kinematic synthesis in analytical form [68][69][70][71][72][73].…”

Section: Analytical Deduction Of Instantaneous Invariants For Complia...mentioning

confidence: 99%

“…Another important instantaneous invariant that is worth defining analytically is the first Bresse's circle (or inflection circle) [68][69][70][71][72]74,75]. It is the locus of points that have an instantaneous rectilinear motion (i.e., have zero normal acceleration).…”

Section: Analytical Deduction Of Instantaneous Invariants For Complia...mentioning

confidence: 99%

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

Iandiorio

Salvini

2023

Micromachines

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“…Instantaneous invariants were introduced by Veldkamp [11] to simplify the study of the curvature of planar point trajectories. For recent discussions of instantaneous invariants, see Roth [12] and Figliolini and Lanni [13].…”

Section: Literature Reviewmentioning

confidence: 99%

A steerable robot walker driven by two actuators

Li,

Liu,

Nguyen

et al. 2023

Robotica

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This article describes a robot walker based on a new single degree-of-freedom six-bar leg mechanism that provides rectilinear, non-rotating, movement of the foot. The walker is statically stable and requires only two actuators, one for each side, to provide effective walking movement on a flat surface. We use Curvature Theory to design a four-bar linkage with a flat-sided coupler curve and then adds a translating link so that walker foot follows this coupler curve in rectilinear movement. A prototype walker was constructed that weighs 1.6 kg, is 180 mm tall, and travels at 162 mm/s. This is an innovative legged robot that has a simple reliable design.

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“…Other authors—especially in books written for mechanical engineers [ 4 – 6 ]—put more emphasis on the time-based treatment of the important concepts, i.e., the main results are derived and formulated by using position, velocity and acceleration vectors. Geometrical kinematics has several advantages over the time-based approach in terms of mathematical elegance and rigor [ 7 ]. However, the learning (and teaching) of geometrical methods requires the application of advanced mathematical tools.…”

Section: Introductionmentioning

confidence: 99%

Analysis of pole acceleration in spatial motions by the generalization of pole changing velocity

Csernák

2019

Acta Mech

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It is well known in planar kinematics of rigid bodies that the acceleration of the material point coinciding with the instantaneous center of rotation (or pole) is perpendicular to the so-called pole changing velocity. In the present paper, the concept of pole changing velocity is generalized to spatial motions. Using this result, the acceleration of the material points along the instantaneous screw axis can be expressed in a straightforward way, without the tools of advanced differential geometry.

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On the advantages of instantaneous invariants and geometric kinematics

Cited by 22 publications

References 10 publications

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

Elasto-Kinematics and Instantaneous Invariants of Compliant Mechanisms Based on Flexure Hinges

A steerable robot walker driven by two actuators

Analysis of pole acceleration in spatial motions by the generalization of pole changing velocity

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