Abstract
In this article, a novel fully compliant spherical four-bar mechanism is introduced and its generalized design methodology is proposed. The original fully compliant mechanism lies on a plane at the free position (undeflected position); therefore, it has the advantages of ease of manufacturing, minimized parts, and no backlash. First, the mobility conditions of the mechanism are obtained. The dimensions of the mechanism are optimally calculated for maximum output rotation, while keeping the deflection of flexural hinges at an acceptable range. Using an optimization method, design tables are prepared to display the relationship between arc lengths and corresponding deflections of flexural hinges. Input–output torque relationship and stresses at compliant segments are obtained analytically. A mechanism dimensioned by this novel design method is analyzed by a finite element analysis method, and the analytical results are verified. Finally, the mechanism is manufactured and it is ensured that the deflections of the compliant segments are consistent with the theoretical results.
Highlights
The moving links of spherical mechanisms are constrained to the concentric surfaces of a sphere, and they generate three-dimensional movements.[1]
The compliant segments are replaced by an equivalent system of torsional springs, joints, and links using a pseudo-rigidbody model (PRBM) technique.[9]
The optimization routine derived, the conditions listed and the results shown in Tables 1– 7 can be very useful during the initial design stage of a fully compliant spherical four-bar mechanism that performs input–output motion transmission
Summary
The moving links of spherical mechanisms are constrained to the concentric surfaces of a sphere, and they generate three-dimensional movements.[1]. The conditions that satisfy the planar state of the design, mobility conditions of rigid segments, and limitations of the deflections of compliant segments are determined. If the value a3 is not specified, it mostly converges to the minimum value of 10° during the optimization for a slightly larger Df. Note that the radius of the arc measured from the sphere center that defines the overall size of the mechanism (R) is a free parameter and that can be arranged in combination with the length of the compliant segments. The optimization routine derived, the conditions listed and the results shown in Tables 1– 7 can be very useful during the initial design stage of a fully compliant spherical four-bar mechanism that performs input–output motion transmission. The maximum stress at compliant segments with zero output torque is determined from equation (27)
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