Fractional analysis of induced resonance effects in the spherical motion of a rigid body with flywheels

Proposed in this paper is a general methodology applicable to the synthesis of spherical motion generators in the presence of an incomplete set of finitely separated attitudes. The spherical rigid-body guidance problem in the realm of four-bar linkage synthesis can be solved exactly for up to five prescribed attitudes of the coupler link, and hence, any number of attitudes smaller than five is considered incomplete in this paper. The attitudes completing the set are determined to produce a linkage whose performance is robust against variations in the unprescribed attitudes. Robustness is needed in this context to overcome the presence of uncertainty due to the selection of the unspecified attitudes, that many a time are specified implicitly by the designer upon choosing, for example, the location of the fixed joints of the dyads. A theoretical framework for model-based robust engineering design is thus, recalled, and a methodology for the robust synthesis of spherical four-bar linkages is laid down. An example is included here to concretize the concepts and illustrate the application of the proposed methodology.

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A Pseudo-Rigid-Body Model for Spherical Mechanisms: The Kinematics and Stiffness of a Compliant Curved Beam

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49769 ◽

2008 ◽

Author(s):

Alejandro Leo´n ◽

Saurabh Jagirdar ◽

Craig P. Lusk

Keyword(s):

Rigid Body ◽

Curved Beam ◽

Beam Angle ◽

Element Analysis ◽

Body Model ◽

Spherical Mechanisms ◽

Characteristic Radius ◽

Rigid Body Model ◽

Spherical Mechanism ◽

Spherical Motion

A pseudo-rigid-body model (PRBM) which describes a class of curved compliant beams in terms of spherical mechanism kinematics was developed. The topology of the spherical compliant segment and its rigid-body equivalent were chosen to be analogous to planar models. The nomenclature for the spherical PRBM was also chosen to facilitate comparison with planar models. The motion of the compliant segment was calculated Finite Element Analysis and the PRBM parameters were determined. The characteristic radius and parametric angle coefficient were found to decrease as the angle subtended by the beam increases. The kinematic and elastic parameterization limits of the model increase with increasing beam angle. The stiffness of the beam is described by two separate spring elements, which describe the appropriate combination of moment and force which produces spherical motion. A previous planar PRBM is shown to be the small angle limit of the new spherical PRBM.

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Higher-Order Path Curvature in Spherical Kinematics

Journal of Engineering for Industry ◽

10.1115/1.3438198 ◽

1973 ◽

Vol 95 (2) ◽

pp. 612-616 ◽

Cited By ~ 13

Author(s):

A. T. Yang ◽

B. Roth

Keyword(s):

Rigid Body ◽

Higher Order ◽

Numerical Examples ◽

Characteristic Numbers ◽

Spherical Curve ◽

Spherical Linkages ◽

Path Curvature ◽

Spherical Motion

Characteristic numbers are derived which define a spherical curve, within a stretch rotation, to a given order. The loci of all points, which have the same characteristic numbers, under rigid body spherical motion are studied. These results are useful for synthesis and analysis of spherical linkages. The theory is illustrated by numerical examples for the motion of rolling cones and a spherical turning-block linkage.

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