Hexapod Flexure Stress

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Hexapod Flexure Stress
Michael Sholl 25 April 2003 Rev B.
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Introduction

• Dave Pankow did excellent review of hexapods
• HEXAPODS for FUN PROFIT a brief RD
  inspired web search
• Hexapod 6 legs, 6 DOF
• By changing leg lengths, user may raise,
• lower, shift, tip, tilt, and rotate

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Stewart Platform/Hexapod
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Direct Kinematic Solution of Stewart Platform

• Given change in leg length,
• how does platform move?
• Each leg has
• Given length
• Constraints of base
• Constraints of mirror
• Nonlinear equations
• Multiple solutions exist
• Not straightforward

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Inverse Kinematic Solution

• Given position change in mirror,
• what are leg lengths?
• Easy to solve
• Rotate and translate mirror points
• Determine lengths directly

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Calculation

• State vector s(X, Y, Z, ?x, ?y, ?z)T
• Length vector l(l1, l2, l3, l4, l5, l6)T
• Influence matrix

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Influence Matrix

• Computed with centered differences
• Spatial tiny1mm
• Angular tiny1 arcmin
• Lengths computed
• (?l)P(?s)
• Approximation to direct solution
• P-1(?l)P-1P(?s)
• or (?s) P-1(?l)

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Stresses in flexures

• If flexures are used at joints?stresses induced
• What are their magnitudes?
• Sample case
• 0.5m diameter base
• 0.433m diameter base
• Height20cm
• Moment in flexure is proportional to the
• angle of rotation of the joint, relative to
• that of an unperturbed system
• These stresses depend on hexapod geometry

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Strain (Rotational) in flexures

• Generally, strains are higher on mirror joints

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Inverted Hexapod Strains

• Generally, strains are higher on mirror joints