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Design and Characterization of a Precision Motion System

Course of Design of Precision Engineering

Group C
Alberto Andreetto (267439), Isacco Libera (268110), Paolo Rossi (265871), Daniele Trisotto (267254)

25 June 2026

Project Objectives

  1. Design a precision motion de-amplifier

  1. Static calibration of a precision motion amplifier

Calibration performed on an existing setup.

Design a Precision Motion De-Amplifier

Design Workflow

Product Definition

Customer needs:

  • Straight input and output motion
  • De-amplification ratio \(\text{OUT}:\text{IN} = 1:20\)
  • Linear relationship with maximum deviation \(\leq 5\%\)
  • Reversible motion transmission

Application constraints:

  • Input stroke \(\leq 10 \,\mathrm{mm}\)
  • Input force \(\leq 0.1 \,\mathrm{N}\)
  • Space envelope \(\leq 200 \times 200 \times 20 \,\mathrm{mm}\)
  • Flat sensing surface \(\geq 5 \times 5 \,\mathrm{mm}\)
  • Kelvin clamp support

Quality Function Deployment (QFD)

  • Translate customer needs into concrete design criteria
  • Needs \(\rightarrow\) Requirements (comprehensible by customers)
  • Requirements \(\rightarrow\) Specifications (engineering language)

QFD won’t be entirely explained, since it was already presented in class.

Product Decomposition

  • Existing systems decomposed into atomic functions
  • Independent analysis performed by each team member
  • Useful to improve the knowledge of the topic
  • Example shown on the right

Functional Decomposition

  • Functional architecture derived from system requirements
  • System decomposed into atomic functions
  • Hierarchical organization of functional blocks

Morphological Combination

  • Atomic functions combined into a morphological map of the system

Theory of The Resolution of Inventive Problems (TRIZ)

  • Identification of engineering contradictions
  • Separation between conceptual solution and implementation
  • Application of the 40 TRIZ inventive principles
  • Contradictions derived from system requirements

Example of Contradiction Resolution

Concepts Generation

  • Product decomposition used as a knowledge base for concept generation
  • Morphological map translated into multiple conceptual solutions
  • Emphasis on system architecture rather than implementation details
  • Preliminary calculations and simulations used for concept validation

Each figure is labeled above with its corresponding concept number.

Single-Stage Mechanical Concept

  • Motion amplification achieved through gear transmission
  • Gear mechanisms unsuitable for high-precision applications due to backlash and friction

Multi-Stage Compliant Mechanism Concepts

  • Multi-stage motion transmission and amplification
  • Elastic deformation enables high repeatability
  • Straight-line motion achieved through structural symmetry
  • Motion amplification through lever mechanisms
  • Linear input-output relationship enabled by lever kinematics

Single-Stage Compliant Mechanism Concepts

  • One stage only, integrating motion transmission and amplification
  • Motion Amplification achieved through two parallel levers
  • Same kinematic and compliant principles as multi-stage architectures

Lever-Cascade Compliant Mechanism Concepts

  • Motion amplification through several levers in series
  • Same kinematic and compliant principles as multi-stage architectures

Robust Decision-Making

  • System requirements adopted as decision criteria
  • Belief maps used by each group member to evaluate the capability of each concept to satisfy the design criteria
  • Decision matrix used for concept ranking and comparison

Selected Concept

  • Lever-Cascade Compliant Mechanism Concept 2 selected from the decision matrix evaluation
  • The selected concept was then further analysed and modelled

Modeling Workflow

Kinematic Design

  • Lever-based mechanism architecture:
    • linear displacement de-amplification
    • reversible kinematic behaviour
  • Straight-line motion ensured by structural symmetry

Dynamic Design

  • Elastic deformation enables:
    • high repeatability
    • system reversibility
  • Flexure hinges adopted to implement joints
  • Hinge optimization:
    • Leaf hinges: low stiffness, high angular excursion, less precise motion
    • Circular hinges: high stiffness, limited angular excursion, more precise motion

Material Selection

  • Material selection supported by Ashby Map
  • High yield strength identified as a key requirement \(\Rightarrow\) Beryllium-Copper selected to avoid plastic deformation

Simulation Results

Gain OUT : IN \(1:20\) at \(y_{in}=10\,\mathrm{mm}\)
Maximum linearity deviation \(0.7\%\ (0.0035\ \mathrm{mm})\)
Maximum space envelope \(199.5 \times 174.87 \times 8\ \mathrm{mm}\)
Maximum input force \(1.07\ \mathrm{N}\)

The deviation from linearity is calculated over the full-scale (\(FS\)) output range: \[ \Delta_{\text{linearity}} = \frac{|y_{\text{sim}} - y_{\text{interp}}|}{FS} \times 100 \]

Simulation Results

  • Attenuation behaviour with resonance at \(30 \,\mathrm{rad/s} = 4.77 \,\mathrm{Hz}\)
  • Strong post-resonance attenuation and phase delay

Static Calibration of a Precision Motion Amplifier

Measured System and Experimental Setup

  • Passive vibration-isolation bench
  • Kelvin-clamp precision mounting with a tension spring for attachment
  • Precision-screw manual actuation
  • LIF-based input/output displacement measurement

Effect of Noise

  • Negligible noise contribution:
    • Sensor drift: \(\sim 10^0 \,\mathrm{nm/s}\)
    • Stochastic contribution: \(\sim 10^1 \,\mathrm{nm}\) with \(95\%\) confidence level
  • ACF and FFT analyses therefore considered unnecessary

Operating displacements were on the order of \(\sim 10^{0}\,\mathrm{mm}\) (input) and \(\sim 10^{-2}\,\mathrm{mm}\) (output); hence, noise contribution was considered negligible.

Static Calibration Results

  • Second-order model adopted to fit data: \[ y_{i,k} = \beta_0 + \beta_{k} + \beta_1 x_{i,k} + \beta_2 x^2_{i,k} + \varepsilon_{i,k} \] where \(i\) index of measurement and \(k\) index of motion direction.

  • Residuals normality: p-value \(= 0.15\) (Shapiro-Wilk test)

  • Maximum deviation from linearity \(\Delta_{\text{linearity}} = 0.01\%\)

Table 1: Regression coefficients and standard errors.
Term Estimate Std. Error
\(\beta_0\ \mathrm{(mm)}\) \(-3.61 \cdot 10^{-4}\) \(6.28 \cdot 10^{-6}\)
\(\beta_{forward}\ \mathrm{(mm)}\) \(-4.02 \cdot 10^{-5}\) \(3.24 \cdot 10^{-6}\)
\(\beta_1\ \mathrm{(adim)}\) \(4.89 \cdot 10^{-2}\) \(5.16 \cdot 10^{-6}\)
\(\beta_2\ \mathrm{(1/mm^2)}\) \(-1.67 \cdot 10^{-4}\) \(9.51 \cdot 10^{-7}\)

Similarly to the modeling section, the deviation from linearity is calculated over the full-scale (\(FS\)) output range: \[ \Delta_{\text{linearity}} = \frac{|y_i - \hat{y}_i|}{FS} \times 100 . \]

Calibration Conclusions

  • Negligible offset and direction bias coefficients (\(\beta_0\), \(\beta_{\mathrm{forward}}\)): limited hysteresis effects
  • Minimal quadratic contribution \(\beta_2\)
  • Dominant linear coefficient \(\beta_1 = 4.89 \cdot 10^{-2} \approx \frac{1}{20}\), confirming high linearity

AI Usage

AI-based tools were employed to support layout refinement, visual content generation, and presentation optimization.

In particular:

All generated materials were reviewed and validated by the authors.

Thank you for your attention!