EDCM: Engaging–Disengaging Compliant Mechanism

• EDCM is a bistable compliant mechanism that uses elastic deformation in shallow arches to transition between an engaged (infinite stiffness) and a disengaged (near-zero stiffness) state.
• Its design leverages analytical buckling theory and shallow arch beam modeling to precisely tailor actuation force and snap-through travel for robust functionality.
• Experimental and FEA validations confirm its repeatable performance and reliability in applications ranging from robotics to adaptive metamaterials and mechanobiology.

The Engaging–Disengaging Compliant Mechanism (EDCM) is a class of bistable mechanical architectures that utilize elastic deformation—primarily in shallow arches—to enable switching between two extreme stiffness states: theoretically infinite stiffness (“engaged” or locked) and near-zero stiffness (“disengaged” or unlocked). This mechanism offers rapid, reliable, and repeatable transitions in mechanical response, with applications spanning robotics, MEMS, reconfigurable metamaterials, and mechanobiology.

1. Fundamental Principle and Architecture

The EDCM operates between two points, A and B, in a compliant linkage and can instantaneously switch the transmission of motion or force:

• Engaged/Locked state: Displacement at A is identically transferred to B, i.e., infinite longitudinal stiffness.
• Disengaged/Unlocked state: A and B move independently, yielding zero longitudinal stiffness.

The canonical EDCM architecture comprises three bistable arches:

• One central arch aligned along AB.
• Two side arches oriented normal to AB.

In the unlocked state, the central arch is unconstrained, allowing snap-through from one stable form to another under a force $f_s$ at its midspan, which produces a travel $u_{tr}$ and decouples A and B. In the locked state, both side arches snap inward, driving interlocked arms under inclined clips on the central arch; this geometrically restricts midspan motion and causes the central arch to resist further displacement with infinite stiffness.

2. Analytical Dimensioning and Design Equations

EDCM dimensioning leverages shallow-arch beam theory and critical buckling analysis, as detailed in Palathingal & Ananthasuresh (2017) and implemented in (Srivastava et al., 8 Nov 2025). For a shallow, fixed–fixed arch of span $l$, mid-rise $h_{\text{mid}}$, modulus $E$, cross-sectional area $A = bt$, and second moment $I = bt^3/12$:

• Buckling (critical axial) load:

$N_{\text{cr}} = \frac{\pi^2 EI}{l^2}$

• Potential energy under end-shortening load $N$:

$$\Pi[y(x)] = \frac{EI}{2} \int_0^l (y^{\prime\prime}(x))^2 dx - N \int_0^l (\sqrt{1+(y'(x))^2} - 1) dx$$

• State transitions (snap-through condition): Equilibrium and stability are enforced by

$$\left. \frac{\partial \Pi}{\partial \delta}\right|_{f_s} = 0 \qquad \left. \frac{\partial^2 \Pi}{\partial \delta^2}\right|_{f_s} = 0$$

• Closed-form dimensioning:

$$\frac{f_s l^3}{EI h_{\text{mid}}} = 1486.57 \qquad \frac{u_{tr}}{h_{\text{mid}}} = 1.98$$

with locking condition

$$k_{\text{locked}} = \lim_{\delta \to 0} \frac{N}{\delta} = \infty$$

Here, $f_s$ and $u_{tr}$ are the switching force and snap-through travel; these directly determine actuation force requirements and unlocking/locking thresholds.

Design parameter effects:

• Span $l$: Longer span lowers $f_s$ and increases travel; trade-off between actuation ease and locked-state rigidity.
• Mid-rise $h_{\text{mid}}$: Scales both travel and switching force proportionally; higher $h_{\text{mid}}$ increases travel and actuation force.
• Cross-section $t$: $I \sim t^3$; increased thickness greatly raises $f_s$.
• Material modulus $E$: Higher $E$ raises $f_s$, does not affect normalized travel.

This analytic framework allows prescribed $\{f_s, u_{tr}\}$ for both central and side arches, facilitating tailored EDCM response for domain-specific applications.

3. Numerical and Experimental Validation

Finite element and experimental validation (ABAQUS with C3D8R, NLGeom=ON, Onyx polymer, $E=2.4$ GPa, $\nu=0.3$) demonstrate EDCM performance:

• FEA (locked state): $k_{\text{locked}} > 83$ N/mm ($<0.6$ mm deflection under 50 N load).
• FEA (disengaged state): $f_s \approx 17$ N, $u_{tr} \approx 16$ mm.
• Yield margin: Maximum stress $<20$ MPa, well below material yield.
• Prototype metrics: $f_s = 17.0 \pm 0.5$ N, $u_{tr} = 15.8 \pm 0.4$ mm; locked stiffness $>80$ N/mm, unlocked $1.1$ N/mm; side arch switching force $70 \pm 2$ N; reliable bistability over $>100$ cycles.

The close match ($<$5% error) between analytic and FE/experimental values substantiates the predictive design equations.

4. Topological Optimization and Generalization

Topology optimization of contact-aided compliant mechanisms (CCMs) extends EDCM design into multi-kink, switching networks (Kumar et al., 31 Oct 2024, Reddy et al., 2020). The CCM paradigm uses negative circular (and generalized) masks to simultaneously remove material and generate rigid contact surfaces. Hexagonal element parameterization and curvature-based boundary smoothing yield robust segment-to-segment contact models.

• Objectives: Fourier shape descriptor (FSD) minimization matches output trajectories to prescribed multi-kink curves, enabling sequential engagement/disengagement in compliant switches.
• Design variables: Both binary (presence/absence, contact indicator) and continuous (geometry, force) overlaid for optimization.
• Contact modeling: Frictionless/adhesionless, augmented Lagrangian with penalty law; compliance matrix dynamically updated as contacts/kinks engage.
• Performance metrics: Shape error $\zeta_s = 2.398\%$, length error $\zeta_l = 7.26\%$; force thresholds set for each kink/engagement.
• Manufacturing: Proposed designs emphasize monolithic architecture with only active contact surfaces fabricated; slender flexural members from hex/smoothing scheme.

Such methodologies provide formulaic recipes for embedding EDCMs within broader compliant architectures, with prescribed force thresholds and robust geometric response.

5. Application Domains and Mechanical Functionality

EDCMs are used across fields requiring tunable, high-contrast mechanical response:

• Robotics: Joint locking/release in manipulators and legged platforms.
• Micro/nanosystems (MEMS): Shock isolation by rapid stiffness switching under vibration.
• Metamaterials: Embedding EDCM cells for reconfigurable in-plane stiffness and Poisson’s ratio.
• Mechanobiology: Cell-culture substrates with invertible Poisson’s ratio and tunable stiffness (Sebastian et al., 11 Nov 2025).

In cell-culture substrates, EDCMs are integrated with re-entrant beam networks to switch between:

• Negative Poisson’s effect ($\mu > 0$, disengaged): Lateral opening under tension, zero stiffness.
• Positive Poisson’s effect ($\mu < 0$, engaged): Lateral contraction, infinite stiffness.

Analytical models (based on Castigliano’s theorem) correlate stretch ratio $\mu$ and stiffness $K$ to geometry; engineered units can achieve in-situ inversion of Poisson’s ratio and repeatable stiffness switching, facilitating dynamic studies of cellular mechanotransduction.

6. Alternate Designs, Lessons, and Customization Recipes

Three alternate EDCM designs were iterated:

• Single-arch/latch clip: Momentary lock, poor re-locking.
• Hourglass clip: Easier return, imperfect kinematic lock.
• Passive perpendicular snap-backs: Easier return, incomplete stiffness.

Final design employs two actively bistable side arches, rigid arms locking a central clip, eliminating free play and achieving bidirectional locking. Reliable locking mandates positive kinematic constraints from bistable elements and minimized clip–arm gap ($<0.1$ mm).

Design recipe for customization:

1. Set desired $\{f_s, u_{tr}\}$ for central/side arches.
2. Solve for $h_{\text{mid}}$ given $u_{tr}$, select $l$, $b$, $t$ to satisfy

$$f_s = \frac{1486.57\,E\,b\,t^3\,h_{\text{mid}}}{12\,l^3},\quad u_{tr}=1.98\,h_{\text{mid}}$$

1. Achieve minimal gap tolerance in lock.
2. Validate via large-deformation FEA (NLGeom=ON) for stress/clearance.

7. Limitations, Generalizations, and Future Directions

Limitations and assumptions include:

• Quasi-static, frictionless contact; dynamic snap-through, frictional latching merits further modeling.
• Linear elastic beam theory; plasticity, hysteresis not modeled.
• 2D mask shapes; full 3D volumetric generalization via polyhedral masks is open.
• Micromechanical aspect-ratio constraints and fabrication tolerances (e.g., $t \geq 3\,\mu$m).

A plausible implication is that EDCM-based switches can be further enhanced by incorporating general contact-surfaces (elliptical/rectangular, non-circular), dynamic or rate-dependent contact models, and hybrid material systems. The embedding of EDCMs in topology-optimized compliant networks opens avenues for complex, programmable mechanical switching in advanced applications.