TB
T. Baaij
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Compliance Matrix Mapping Method
A Hybrid Modeling Method for Fast, Top-Level Design of Large-Range Planar Compliant Mechanisms
This master’s thesis was carried out as part of the SilkTouch Project, a collaborative research initiative between Delft University of Technology and VDL ETG Technology & Development B.V. My specific objective was to develop and investigate a mechanism that can operate a vacuum transfer door without generating contamination. This requirement naturally directed the research towards compliant mechanisms, which generate motion through elastic deformation rather than sliding or rolling contact.
The literature study therefore reviewed vacuum transfer door technology and compliant rotary joints for this application. It showed that suitable joints must combine high mobility with high off-axis stiffness, but that quantitative comparison data is limited. It also identified two relevant door-motion types, L-motion and flapping, which provided the starting point for the main research.
The main research initially continued from this application by exploring linkage topologies for compliant mechanism synthesis. However, the large motion range made parasitic motion, complex loading and the coupling between kinematic and structural behaviour too important to treat as secondary effects. As a result, the focus shifted from designing one specific door mechanism towards developing a modelling approach for large-range planar compliant mechanisms.
This led to the compliance matrix mapping method (CMMM), a reduced-order method intended to support fast early-stage evaluation while still accounting for large rotations, parasitic motion and stiffness behaviour. Comparisons with finite-element reference models showed that CMMM can reproduce the main trajectory and stiffness trends with substantially lower computation time, while larger deviations occur for more complex mechanisms and sensitive translational components. A case study on a particle-free vacuum transfer door further showed that mechanism selection cannot be based on topology alone: stiffness, joint mobility, footprint and implementation constraints must all be considered. Overall, the thesis establishes CMMM as groundwork for early-stage design of large-range planar compliant mechanisms, while further refinement, broader comparison and experimental validation remain necessary. ...
The literature study therefore reviewed vacuum transfer door technology and compliant rotary joints for this application. It showed that suitable joints must combine high mobility with high off-axis stiffness, but that quantitative comparison data is limited. It also identified two relevant door-motion types, L-motion and flapping, which provided the starting point for the main research.
The main research initially continued from this application by exploring linkage topologies for compliant mechanism synthesis. However, the large motion range made parasitic motion, complex loading and the coupling between kinematic and structural behaviour too important to treat as secondary effects. As a result, the focus shifted from designing one specific door mechanism towards developing a modelling approach for large-range planar compliant mechanisms.
This led to the compliance matrix mapping method (CMMM), a reduced-order method intended to support fast early-stage evaluation while still accounting for large rotations, parasitic motion and stiffness behaviour. Comparisons with finite-element reference models showed that CMMM can reproduce the main trajectory and stiffness trends with substantially lower computation time, while larger deviations occur for more complex mechanisms and sensitive translational components. A case study on a particle-free vacuum transfer door further showed that mechanism selection cannot be based on topology alone: stiffness, joint mobility, footprint and implementation constraints must all be considered. Overall, the thesis establishes CMMM as groundwork for early-stage design of large-range planar compliant mechanisms, while further refinement, broader comparison and experimental validation remain necessary. ...
This master’s thesis was carried out as part of the SilkTouch Project, a collaborative research initiative between Delft University of Technology and VDL ETG Technology & Development B.V. My specific objective was to develop and investigate a mechanism that can operate a vacuum transfer door without generating contamination. This requirement naturally directed the research towards compliant mechanisms, which generate motion through elastic deformation rather than sliding or rolling contact.
The literature study therefore reviewed vacuum transfer door technology and compliant rotary joints for this application. It showed that suitable joints must combine high mobility with high off-axis stiffness, but that quantitative comparison data is limited. It also identified two relevant door-motion types, L-motion and flapping, which provided the starting point for the main research.
The main research initially continued from this application by exploring linkage topologies for compliant mechanism synthesis. However, the large motion range made parasitic motion, complex loading and the coupling between kinematic and structural behaviour too important to treat as secondary effects. As a result, the focus shifted from designing one specific door mechanism towards developing a modelling approach for large-range planar compliant mechanisms.
This led to the compliance matrix mapping method (CMMM), a reduced-order method intended to support fast early-stage evaluation while still accounting for large rotations, parasitic motion and stiffness behaviour. Comparisons with finite-element reference models showed that CMMM can reproduce the main trajectory and stiffness trends with substantially lower computation time, while larger deviations occur for more complex mechanisms and sensitive translational components. A case study on a particle-free vacuum transfer door further showed that mechanism selection cannot be based on topology alone: stiffness, joint mobility, footprint and implementation constraints must all be considered. Overall, the thesis establishes CMMM as groundwork for early-stage design of large-range planar compliant mechanisms, while further refinement, broader comparison and experimental validation remain necessary.
The literature study therefore reviewed vacuum transfer door technology and compliant rotary joints for this application. It showed that suitable joints must combine high mobility with high off-axis stiffness, but that quantitative comparison data is limited. It also identified two relevant door-motion types, L-motion and flapping, which provided the starting point for the main research.
The main research initially continued from this application by exploring linkage topologies for compliant mechanism synthesis. However, the large motion range made parasitic motion, complex loading and the coupling between kinematic and structural behaviour too important to treat as secondary effects. As a result, the focus shifted from designing one specific door mechanism towards developing a modelling approach for large-range planar compliant mechanisms.
This led to the compliance matrix mapping method (CMMM), a reduced-order method intended to support fast early-stage evaluation while still accounting for large rotations, parasitic motion and stiffness behaviour. Comparisons with finite-element reference models showed that CMMM can reproduce the main trajectory and stiffness trends with substantially lower computation time, while larger deviations occur for more complex mechanisms and sensitive translational components. A case study on a particle-free vacuum transfer door further showed that mechanism selection cannot be based on topology alone: stiffness, joint mobility, footprint and implementation constraints must all be considered. Overall, the thesis establishes CMMM as groundwork for early-stage design of large-range planar compliant mechanisms, while further refinement, broader comparison and experimental validation remain necessary.
High-tech manufacturing systems often require vacuum sealing with minimal particle contamination. Contactless vacuum sealing avoids wear particles generated by contact at the sealing interface by separating the sealing surfaces with a thin pressurised air film. However, this air film creates a leakage path towards the vacuum outlet and therefore governs sealing performance. This thesis therefore investigates whether leakage towards the vacuum outlet can be reduced by changing the air film geometry. Because direct literature on this type of control in contactless vacuum seals is limited, related thin-film air bearing systems are first explored to identify existing methods for controlling the gas film. Aerostatic thrust bearings form a close analogue for this exploration, because they also rely on a thin pressurised air film to separate two surfaces. The literature study shows that gas film gap control is already used in these systems, mainly to improve bearing performance measures such as stiffness, load capacity and dynamic stability. Existing approaches include passive membrane compensation and active nominal gap height control through preload, for example using weights, magnetic forces or vacuum preload. Active surface deformation has also been investigated, but mainly as a way to improve bearing performance through global conicity control. In these studies, the air film is typically treated as a bearing gap between supply and atmosphere, rather than as a sealing interface with a separate vacuum outlet. The resulting gap control methods therefore do not directly address the mass flow distribution between a vacuum region and the atmosphere. In response to this research gap, the main study investigates active dome shaped surface deformation as a method for controlling the mass flow distribution in a contactless vacuum seal. Instead of using deformation to improve conventional bearing performance criteria, the deformation is used to change the relative flow resistance between the vacuum outlet and the atmospheric boundary. The objective is therefore to determine whether the supplied air can be redistributed between the vacuum outlet and the atmosphere without introducing mechanical contact. To study this, a numerical model based on compressible thin-film flow was developed under choked inlet operation. The model was used to characterise how imposed deformation, system scale, inlet mass flow, inlet position and vacuum outlet radius affect the redistribution of mass flow between the vacuum outlet and the atmosphere. The normalised deformation ΔH/H0 was identified as the key scaling parameter, collapsing the mass flow redistribution responses for different system scales and imposed inlet mass flows onto a single curve. Here, ΔH is the imposed dome shaped deformation and H0 is the initial operating gap height. This collapse holds for a fixed inlet position and vacuum outlet radius, while changing these geometric parameters alters the response curve. The predicted response was then assessed experimentally using a wire actuation mechanism that induced a positive dome shaped curvature in the floating top plate. Because direct vacuum mass flow measurements were not available, the comparison was based on a pressure-derived relative vacuum response. At an initial film gap height of H0 = 48.2 μm and an average deformation of ΔH = 10.7 μm, corresponding to ΔH/H0 = 0.22, the corrected experimental and numerical responses corresponded to vacuum mass flow reductions of 17.5% and 17.7%, respectively. This supports the numerical prediction that positive dome shaped deformation can redistribute the supplied air away from the vacuum outlet in the tested configuration. This demonstrates that active surface deformation can be used to influence the mass flow distribution in the thin gas film, providing a first step towards controlled sealing performance in a contactless vacuum seal.
...
High-tech manufacturing systems often require vacuum sealing with minimal particle contamination. Contactless vacuum sealing avoids wear particles generated by contact at the sealing interface by separating the sealing surfaces with a thin pressurised air film. However, this air film creates a leakage path towards the vacuum outlet and therefore governs sealing performance. This thesis therefore investigates whether leakage towards the vacuum outlet can be reduced by changing the air film geometry. Because direct literature on this type of control in contactless vacuum seals is limited, related thin-film air bearing systems are first explored to identify existing methods for controlling the gas film. Aerostatic thrust bearings form a close analogue for this exploration, because they also rely on a thin pressurised air film to separate two surfaces. The literature study shows that gas film gap control is already used in these systems, mainly to improve bearing performance measures such as stiffness, load capacity and dynamic stability. Existing approaches include passive membrane compensation and active nominal gap height control through preload, for example using weights, magnetic forces or vacuum preload. Active surface deformation has also been investigated, but mainly as a way to improve bearing performance through global conicity control. In these studies, the air film is typically treated as a bearing gap between supply and atmosphere, rather than as a sealing interface with a separate vacuum outlet. The resulting gap control methods therefore do not directly address the mass flow distribution between a vacuum region and the atmosphere. In response to this research gap, the main study investigates active dome shaped surface deformation as a method for controlling the mass flow distribution in a contactless vacuum seal. Instead of using deformation to improve conventional bearing performance criteria, the deformation is used to change the relative flow resistance between the vacuum outlet and the atmospheric boundary. The objective is therefore to determine whether the supplied air can be redistributed between the vacuum outlet and the atmosphere without introducing mechanical contact. To study this, a numerical model based on compressible thin-film flow was developed under choked inlet operation. The model was used to characterise how imposed deformation, system scale, inlet mass flow, inlet position and vacuum outlet radius affect the redistribution of mass flow between the vacuum outlet and the atmosphere. The normalised deformation ΔH/H0 was identified as the key scaling parameter, collapsing the mass flow redistribution responses for different system scales and imposed inlet mass flows onto a single curve. Here, ΔH is the imposed dome shaped deformation and H0 is the initial operating gap height. This collapse holds for a fixed inlet position and vacuum outlet radius, while changing these geometric parameters alters the response curve. The predicted response was then assessed experimentally using a wire actuation mechanism that induced a positive dome shaped curvature in the floating top plate. Because direct vacuum mass flow measurements were not available, the comparison was based on a pressure-derived relative vacuum response. At an initial film gap height of H0 = 48.2 μm and an average deformation of ΔH = 10.7 μm, corresponding to ΔH/H0 = 0.22, the corrected experimental and numerical responses corresponded to vacuum mass flow reductions of 17.5% and 17.7%, respectively. This supports the numerical prediction that positive dome shaped deformation can redistribute the supplied air away from the vacuum outlet in the tested configuration. This demonstrates that active surface deformation can be used to influence the mass flow distribution in the thin gas film, providing a first step towards controlled sealing performance in a contactless vacuum seal.