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Independent Study: Compliant Mechanisms

Christopher Apple

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What’s a Compliant mechanism?

  • a thing that changes a mechanical input (force, torque, energy etc.) into a mechanical output by flexing
    • There can be joints in a compliant mechanism, it just has to flex somewhere
  • To the right are bendy tongs
    • Bendy tongs are a compliant mechanism

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Why an Independent Study?

  • Xbox One Scuf ~ $150
  • Xbox One Elite ~ $150
  • Collective minds Strike Pack $40 + controller

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Why a Compliant Mechanisms Independent study?

  • These are prototypes before independent study
  • Difficulties with pins
  • Attempts at compliant mechanisms are uninformed, empirical design was not getting very far

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What did you actually do for an Independent Study?

  • Read
    • This textbook
    • papers (2 Larry Howell, 1 Hasso Platner, 1 split tube pipe,1 Bayer manual of snap fit design)
  • Delivarables
    • Controller paddles
      • Snap fit joints
    • Equivalent Pseudo Rigid Body Mechanisms
    • Constant Force Gripper
    • this powerpoint presentation

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Why should I care about compliant Mechanisms?

  • Useful for
    • Cost reduction
      • Part number reduction
      • Simplified manufacturing, assembly
      • Joint replacement
      • Reduced maintenance
    • Improved Performance
      • MEMS (Microelectromechanical Systems)
      • Metamaterials and metamechanisms
      • Harsh environment
      • Reduced weight
      • Energy storage
      • Reduced wear

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Flexibility and Deflection

  • Stiffness Strength
  • Because Deflection Failure
  • Flexibiliy Ductility
  • In other words Stiff Brittle

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Pseudo Rigid-Body Model

Helpful Prerequisites

  • Mechanical Engineering Undergrad
  • Robot Geometry helps
  • Analytical Dynamics (greduate level) comes up
  • Graduate courses in Solid Mechanics would probably help
  • More of a Dynamics, Systems and Control (DSC) approach to Compliant Mechanisms
  • Main idea is to approximate flexural segments as joints and otherwise use rigid body mechanics
  • Slight changes are made to skeleton diagrams
    • Flexible segments are thin lines
    • Circles with “X”s are pins with torsional springs

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Pseudo Rigid-Body Model Pins

Pictures from the book

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Pseudo Rigid-Body Model Pins

Picture From the book

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Pseudo Rigid-Body Model Sliders

Pictures from the book

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Deliverable 1: Equivalent Pseudo Rigid-Body Demo

  • This is a demo of a
    • Short cantilever beam
    • Fixed pinned beam
    • Precurved Fixed-Pinned beam
  • They are designed to have the same spring constant so that they have equivalent motion
  • This demonstrates the differences in designing these compliant pins
  • Each has trade offs

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Deliverable 1: Equivalent Pin Trade offs

  • For same spring constant
  • Short length Cantilever beam
    • Shortest beam
    • Highest stress concentration
  • Fixed Pinned beam
    • Thickest beam
  • Precurved Beam
    • Longest beam (in arc length and from end to end)
    • Thinnest beam
    • Lowest stress concentration

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Deliverable 1: Equivalent Pin Design

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Deliverable 1: Equivalent Pin Design

Precurved Fixed-Pinned

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Deliverable 1: Lessons learned

  • PLA does not have good strength to flexibility
    • In order to have enough flex to feel the PLA is so thin than it is fragile and prone to stress relaxation
    • Even ran into quantization error with the need for a 0.25 mm thick beam and a resolution of 0.2 mm
  • I thought the short cantilever beam would be the thinnest at the same spring constant but the curved fixed pinned beam was
    • This is not only because the arc length effectively makes the beam longer but gamma () is replaced with rho () which is lower
  • When I tried to make the beams the same spring constant K and length from the virtual pin gamma the short beam and fixed pinned beam were defined with the pre-curved beam was over-defined
  • Stress relaxation

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Cantilever Snap Fit Joints

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Torsion Snap Fit Joints

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Annular Snap Fit Joints

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Deliverable 2: Video Game Controller Paddles

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Deliverable 2

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Deliverable 2

Picture from the book

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Deliverable 2: Lessons Learned

  • 3D printingSnapfit joints can be tricky
    • Mechanism’s snap fit joints bend in same plane as applied force because that was how I could print it on the build plate
    • Might replace with alternatives
    • Limited material options makes it hard to make strong but flexible prongs
  • The spring constants carry the same weight for transmitting force
  • There is a tradeoff; stiffer springs means more force per displacement put in but more force out and more energy conserved
  • Print orientation is important for parts not just because of the material properties but even for variations of thicknesses

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Deliverable 2: Results and going forward

  • I have posted this on Pinshape, and while it is functional it’s not really done
    • Still pretty neat though
  • I might change this
    • Replace current snap fit joints with sturdier alternative
    • Change snap on hooks for snap into the battery door
    • Add two more paddles

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Deliverable 3: Constant Force Gripper

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Deliverable 3: Constant Force Gripper Design

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Deliverable 3: Lessons Learned

  1. Mechanism in locked angle
    1. You probably know from undergrad Kin and Dyn that If you do a free body diagram of this mechanism at 180 degrees you realize that this mechanism would lock
    2. I meant to remedy this by having a place to poke the flexing segmenent but the hole is too small
  2. Deflection relative to tolerances - the movement from the generous tolerances on the passive joints are too large compared to the deflection to get much value out of the bending; it’s more like you are wedging the piece in there

The school printer can get much more precise tolerances than my CTC bizer

  1. Deflection is a bit small to see - may have chosen bigger deflection than pcb
  2. Relative rigidity - “rigid” parts are too flexible

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Multistable/Bistable Mechanisms

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https://youtu.be/20gVvICfJj4

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Optimal Synthesis with Continuum Models

  • Sometimes referred to interchangeably topological optimization
  • The book had only 1 chapter on this, done by guest authors
    • Did not seem to be Larry Howell’s focus
  • More of a Solid Mechanics, Design and Manufacturing (SMDM) approach to compliant mechanisms
  • More Computationally and software intensive
  • Probably useful for Metamechanisms

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Conclusion/Big Lessons

  • Once you know to look for Compliant Mechanisms you can see their widespread use
  • 3D printing seems like a good way of applying compliant mechanisms because of the rapid prototyping but it does complicate things
    • Limited printing materials
    • Inconsistent material properties
    • Limitation in geometry because of orientation on the build plate
  • Compliant Mechanisms are niche but useful for a reason
    • Require interdisciplinary knowledge
    • Couples Kinematics and Kinetics more than usual Rigid Body Design

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References

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