Laser Forming of Compliant Mechanisms

Compliant mechanisms are being designed with increased complexity requiring more precise and flexible solutions to achieve desired performance [1,2]. They have been used as a solution for systems that require simplicity in form while retaining complex motion, but such mechanisms are challenging to form and assemble on small scales [3]. Many such mechanisms require feature precision on the mesoscale (0.1–5 mm) and low macroscale (5–100 mm), which can be difficult to create [4]. Metals are used in compliant mechanisms for their various desirable properties (e.g., electrical/thermal conductivity, durability, recyclability, and cleanability).

Metal 3D printing is a current method of fabricating metal compliant mechanisms, but the technology can result in component anisotropy, high production costs, and a discontinuous manufacturing process that present challenges in some applications [5]. However, there is some research starting to be done on improving additive manufacturing for metal compliant mechanisms [6]. Outside of additive manufacturing, metal is difficult to machine on the mesoscale, with electrical discharge machining (EDM) being one of the few viable options. EDM has been shown to successfully manufacture extremely small metal compliant mechanisms [7]. EDM has also been used to manufacture bi-stable compliant mechanisms on the macroscale out of bulk metallic glass [8]. However, EDM requires expensive and complex machinery with a high tool wear ratio and low surface quality [9]. Additional advances are needed to fabricate compliant mechanisms and flexible systems on the mesoscale in thin sheet metal.

Laser forming is a fabrication process involving the controlled deformation of a workpiece through the use of a laser to introduce plastic thermal stresses and is typically used on large scales and very simple geometries. However, this process has recently been explored on the mesoscale to fold rigid structures [10]. But without moving components, the ability of these structures to form more complex mechanical systems is limited. Fortunately, laser forming has a potential to fabricate more than just rigid shapes and structures.

This work develops laser forming as a method for creating simple compliant mechanisms and shows how this fabrication method could be useful in manufacturing such mechanisms in sheet metal on the mesoscale. To achieve this goal, the research focuses on the design, fabrication, and force–deflection testing of three simple compliant mechanisms. The “building-block” components of these designs will be broken down into features and discussed. These simple features will serve as the basis of two more complex mechanism applications. These applications will demonstrate the first usable compliant mechanisms created by laser forming.

This research space requires an understanding of the current state of the art of compliant mechanisms and laser forming, especially how they each relate to thin sheet metal. The field of compliant mechanisms is quite broad and covers a variety of sizes (micro to macro) and many different kinds of materials. Compliant mechanisms designed to be fabricated in a flat plane have been explored to various degrees in plastics and metals. Much research has been done on laser forming as well, including different kinds of metals with sheets of various thicknesses.

Compliant mechanisms consist of flexible members in mechanical systems and can serve as replacements for traditional mechanical components. A variety of materials and structures have been used to design compliant mechanisms, though metals and polymers are common materials used to develop compliant components. The principles of compliant mechanisms can be used to change existing mechanical designs using rigid-body replacement [11] or to develop innovative new solutions to mechanical problems. Compliant components can enable the folding of materials into different configurations [12]. Such mechanisms are a way to achieve mobility with flexible members without the need for mechanical joints and have been applied at both the micro and macro scales.

Compliant mechanisms have been more recently used to approximate origami systems because of their flexibility [13]. As such, flexible members can be used for many possibilities when they are substituted for typically rigid members so that they can be utilized in unique ways to achieve complex behavior [14]. Techniques for the fabrication of such systems are valuable because all components are folded from a flat configuration into a desired shape.

The current methods of manufacture for metal compliant mechanisms are 3D printing (e.g., sintering, powder metallurgy), EDM, stamping, milling, and manual cutting and bending. Each method has inherent advantages and disadvantages. 3D printing metals is time consuming, expensive, and ineffective for the production of thin, smooth structures. EDM was demonstrated by Miller et al. [7] to create thin, compliant mechanisms. While EDM does not require hard tooling, it requires large moving systems and electrically conductive metal to work. Stamping is tedious because many progressive dies must be made for each unique shape. Milling can be precise if automated, but thin features are difficult to manufacture without destroying them with high forces. Another complex manufacturing method for metal compliant mechanisms was proposed by Hayes et al. with the lost mold-rapid infiltration-forming process [4]. Manual cutting and bending by hand is imprecise, labor intensive, and impractical for large-scale production. Traditional fabrication tends to perform better on parts with a lower aspect ratio (overall size to minimum feature), while compliant mechanisms typically require thin dimensions of the high aspect ratio (overall size to compliant feature thickness).

Current fabrication processes for compliant mechanisms do not require the motion of the features on the workpiece to move them to their final position.

The sheet metal that is machined in such a way that complete compliant out-of-plane mechanisms are formed is only starting to be explored. However, compliant mechanisms have been created, so that after fabrication, they can fold out of a single plane and are called “lamina emergent mechanisms” (LEMs) [15]. These mechanisms are manufactured in a single plane (typically with polymers, but also with sheet metal), and their final manufactured shape is also still in-plane. Only when actuated, do these mechanisms move out of their original plane.

While mechanisms like LEMs that can bend out-of-plane after manufacture have been examined, manufacturing sheet metal compliant mechanisms to have geometries out of plane has not readily been explored. Because of the difficulty in fixturing thin sheet metals to prevent damage during fabrication, traditional manufacturing methods for metal compliant mechanisms are not robust enough to create intricate flexures without compromising the structural and mechanical integrity of the piece.

Laser forming is the specialized use of a laser to induce thermal stresses in metal in ways that cause the metal to bend. Final geometries are achieved by the combined deformation of all of the laser actions [16]. This technology was first described and developed to create rigid shapes out of metal by Geiger and Vollertsen [17]. Laser forming is a very complex process with many parameters and effects, but such aspects have been studied in depth since the method was first introduced [18]. Laser forming has been used to fabricate features on a large scale in the shipbuilding and automotive industries [19], and more recently, methods have been developed to form more complex structures with features on the low end of the macroscale.

Two key methods of laser forming exist, (1) the temperature gradient mechanism (TGM), and (2) the buckling mechanism [20]. Both methods use a laser to induce thermal stresses in the metal. The thermal gradient mechanism introduces just enough stress in the piece to cause a crease to form that bends the metal as the metal cools. The buckling mechanism is based on creating a lateral thermal gradient (a heated membrane region), which pushes outward and causes the membrane to buckle. The buckling direction is random in the absence of other factors and can go up or down [21]. It is possible to control this direction consistently by introducing a pre-strain, but it is difficult to replicate a consistent pre-strain in a more complex pattern. For this reason, the TGM was chosen as the method of laser forming for this work.

Laser forming is a nontraditional manufacturing method that is used to shape materials in ways that are difficult otherwise. Much research has been done to bend metal foams into difficult shapes using laser forming [22–24]. The technology of laser forming has also been used on polymers to achieve complex origami-inspired shapes because of the sequential nature of the method [25]. Such work is useful in understanding how origami- and kirigami-inspired shapes can be achieved with laser forming.

The past work by several of the authors demonstrates laser forming used on thin sheet metals with added complexity, combined forming mechanisms, and hands-free processes [10]. Techniques for large-scale bends were adapted in that work to a small scale with 0.0762 mm thick stainless steel. Rigid structures such as a six-sided cube and a paper-airplane-like shape were formed with both temperature gradient mechanism laser forming and buckling mechanism laser forming [26]. This research provides the groundwork for laser-forming mechanisms designed to bend and flex.

To explore the possibilities that laser forming offers for the fabrication of compliant mechanisms, three simple existing compliant mechanisms were selected and developed for the laser-forming technique (the parallel-guided mechanism [27], a cross-axis flexural pivot [28], and a lamina emergent torsional (LET) joint array [29,30]), along with two more advanced mechanisms (a split-tube flexure [31] and a bi-stable switch [32]), as shown in the top row of Fig. 1. These five particular compliant mechanisms were chosen because they can be broken down into building-block features to create more complex mechanisms and a more varied nature from each other. The parallel-guided mechanism can demonstrate fixed-guided beam behavior restricted to a single axial degree-of-freedom perpendicular to the compliant beam; the cross-axis flexural pivot can demonstrate fabrication features that have a single rotational degree-of-freedom by layering compliant features through folding; and the LET joint array can show augmentation of torsional beams to restrict undesired motions. The more complex mechanisms—the split-tube flexural pivot and the bi-stable switch—can demonstrate the forming of curved flexible shapes and actuatable systems, respectively. These mechanisms and the features that comprise them can serve as the basis for later, more complex designs and were modeled after existing designs manufactured in other mediums.

The particular desired behaviors for each mechanism are shown in the bottom row of Fig. 1 for the three simple mechanisms and the two more complex mechanisms. The parallel-guided mechanism in Fig. 1(f) undergoes an applied displacement; the cross-axis flexural pivot and LET joint array (Figs. 1(g) and 1(h)) undergo an applied moment; the split-tube flexure is subjected to an applied radial displacement (Fig. 1(i)); and the bi-stable switch is moved to its second stable state with an applied force (Fig. 1(j)).

Each of the mechanisms was designed such that they would fit within a 4.5 by 4.5 cm², as that was roughly the area within which the chosen laser cutter maintained a solid focus. However, larger sizes and areas could be feasible if using lasers with a larger workspace in which they are focused. Two-dimensional patterns were drawn, and laser parameters were assigned to individual lines so the laser cutter would know which segments needed to be cut and which needed to be folded. Laser forming is a subtractive manufacturing method; thus, care is needed when designing a mechanism to be cut and formed out of a single workpiece. Designing patterns for such a process is similar to the art of kirigami, in which a single sheet of paper is cut and folded into shapes. However, instead of hands folding paper, the laser forming process uses a laser to fold a sheet of metal.

The behaviors of compliant mechanisms depend on feature dimensions and feature orientation about a bend axis to perform intended functions (assuming set material properties). For instance, a flexure that has a thickness larger than its width will be much more difficult to bend than the converse scenario. Because the thickness of the sheet metal is set as a constant, other parameters must be changed to achieve the desired behavior.

Laser forming can cut and bend features of a workpiece into configurations that have desired stiffnesses. This can be controlled by the orientation of individual mechanism features. For instance, rigid features can be formed by bending two metal segments into an L-beam shape. Also, compliant flexures can be formed by having the ends of the metal segment perpendicular to rigid sections so that the flexure can be formed by the laser at the two ends, but the flexure itself is simply a thin bending beam. Through techniques like these, the stiffnesses of individual mechanism features can be defined in the design. The left side of Fig. 2 shows how a pattern was designed for it to be laser formed. The laser was programmed to either cut or fold the designated lines and become the folded features shown on the right side of Fig. 2. The rectangular beams denoted by arrow “b” in Fig. 2 are designated as “flexures” or “flexible members” because of their orientation and intended behavior as compliant components of the mechanism. The rectangular beams denoted by arrows “a” and “c” in Fig. 2 are designated as “rigid segments” or “panels” because of their orientation and intended behavior as undeflecting beams in the mechanism.

The laser used was a full spectrum 1060 nm Nd:YAG engraving laser. Laser cuts were made with 50% power at 500 mm/s for 400 loops. To laser form 90 deg folds, the laser was run with 10% power at 30 mm/s for 5 loops and repeated 20 times. Studies have been performed by Sentoku et al. on calculating input parameters to achieve specific laser-formed angles [33] using a CO₂ laser. However, since an Nd:YAG laser was used here, only estimates and iterative design were used to achieve the desired angles. The 316 stainless steel workpiece was 0.0762 mm thick and was held down by a brass frame and magnets for heat dissipation and stability, respectively. The fixture is shown with the laser-formed LET array in Fig. 3. While 0.0752 mm thick 316 stainless steel was used in this work, the thickness range for the laser-formed metal depends on several variables including maximum laser power, scan speed, and thermal conductivity. Moreover, the force–displacement relationship in compliant mechanisms scales inversely with the cube of the thickness (t), as the moment of inertia is determined by I = (bt³)/12.

The process of laser forming is highly sequential, with the laser following a single path at a time. Each feature fabricated can be formed by the laser in specified orders. Thought must be taken in deciding the order in which the features of a mechanism are formed. Figure 4 shows the process of cutting and forming used to cut, orient, and reorient individual features to fabricate a complete laser-formed cross-axis flexural pivot.

The force–deflection relationship for each of the mechanisms was tested using an Instron 3300 tensile tester with an Interface SMT 1-1.1 S-Type load cell affixed. This allowed for millimeter-sized displacements to be applied and the resultant force to be measured. Magnets held the pieces in place to provide a secure ground and to inhibit undesired motion. Each mechanism was tested repeatedly, and multiples of the same mechanism were tested to account for variation between each fabricated piece. A force–displacement curve for each mechanism was developed based on the tests. Figure 5 shows the setup for the test system.

The results for the fabrication and testing for the three simple compliant mechanisms are shown followed by the fabrication results for the two more complex mechanisms.

Three mechanisms, the parallel-guided mechanism, the cross-axis flexural pivot, and the LET joint array, were fabricated and tested to show force–deflection behavior. These mechanisms demonstrate different desirable properties of compliant mechanisms that can be fabricated with laser forming.

Parallel-guided mechanisms allow for in-plane motion, while the flexures remain parallel with each other. The resulting design for a laser-formed parallel-guided mechanism maintains typical components for such a mechanism, including rigid top and bottom segments with flexures on the right and left sides. The most important consideration for designs like this is for the forces applied to not be distributed through the laser-formed creases.

To create compliant segments with desirable behavior and to isolate the motion, the flexible members were oriented to be perpendicular to the direction of motion. Sections at the top and bottom of each flexure were connected to the rigid sections as space is needed for the laser forming to occur. The triangular shapes that share an interface with the flexures shown in Fig. 6(a) accomplish this purpose, and it is these rigid sections from which the flexures are formed. These techniques demonstrate a key aspect of creating laser-formed compliant mechanisms: features can be oriented by the laser to tune their stiffnesses by creating desired cross sections.

The completed mechanism shown in Fig. 6(c) demonstrates a successfully laser-formed piece. The laser was able to cut where specified and fold the flexures to their expected angle. With simple creases like these, the metal is not able to fold past 90 deg, as the laser is directly above the workpiece, and so it could not make focused contact with the metal if material is in the way. Figure 6(b) shows how the mechanism behaves when loaded as intended.

The experimentally tested mechanism exhibits repeatable behavior over multiple tests, with the mean shown in Fig. 7. As expected, the first actuation of the mechanism after fabrication was an outlier in the data because of stresses being relieved in the system, so that data are not shown. However, for each subsequent test, the mechanism displayed a nearly identical force response. Multiple parallel-guided mechanisms were fabricated and tested, with results being consistent with each other. Figure 6(b) shows how the system behaves when loaded. This motion is similar to the expected behavior shown in Fig. 1(f).

Because the creases were subjected to concentrated heat from the laser, the device failed at the fold when overactuated by fracturing along the fold. However, further process development could understand, quantify, and mitigate the damage. It was therefore important to ensure that the force was distributed almost solely through the flexures.

Analytical models shown by Howell [11] for this kind of mechanism can be used to predict motion for idealized parallel-guided mechanisms and do not take into account the unique attributes of laser-formed mechanisms.

The cross-axis flexural pivot is useful because it can simulate a pin joint but with limited rotation, depending on the boundary conditions and material stresses [34]. The design of the laser-formed cross-axis flexural pivot shares many of the building blocks of the laser-formed parallel-guided mechanism. However, the key difference is that the flexures have to overlap and cross each other to perform as desired. To do this, the mechanism design was essentially created by cutting and forming two mirrored sections and then bringing them to interlock with each other and act as a single mechanism. This can be seen in the fully formed mechanism in Fig. 8(c). Note that the rigid segments at the top of both halves overlap each other to join the sections together. To be more effective, these segments should be fixed together (e.g., welded, taped), though it still works desirably even with the imposed constraints as seen in Fig. 8(b). This motion is similar to the expected behavior shown in Fig. 1(g).

The ability to orient flexures to overlap and “cross” shows that it is possible to form a mechanism that performs a single rotational degree-of-freedom even though seemingly disparate features are used. The fact that the rigid sections at the top of the mechanism have been oriented to face each other helps the whole piece maintain its shape with or without loading.

The mechanism was tested by adhering a string to the rigid segments and the measurement device. The string was then pulled and the resultant forces were measured. The curve shown in Fig. 9 demonstrates the relationship between the applied displacement and the measured resultant force.

Analytical models shown by Jensen and Howell [34] for this kind of mechanism can be used to predict motion for idealized systems and do not take into account the unique attributes that laser-formed mechanisms have.

Lamina emergent torsional (LET) joint arrays enable increased bending via the torsional motion of individual beam members and are made up of multiple LET Joints (developed by Jacobsen et al. [35]) in series and parallel. The shape is straightforward to cut and fold using lasers because, unlike the mechanisms shown previously, individual flexures did not need to be formed. Instead, the laser forming was done at the base and to orient flaps out of plane for each of the holes. These flaps reinforce the structure from undesired axes of motion, while still allowing for motion in the desired bending direction. The flaps can also be shortened or removed in areas where reduced torsional stiffness is desired, thus “tuning” the stiffness of the mechanism. Figure 10(a) shows how this mechanism appears once formed. Care must be taken with the laser settings, as cutting and forming so many small shapes so close to each other concentrates heat, and warping occurs more easily.

The array was able to be actuated as intended as demonstrated in Fig. 10(b), which compares to the expected behavior shown in Fig. 1(h). The curve shown in Fig. 11 for the force–displacement relationship demonstrates the average force response for ten repeated tests on a laser-formed LET joint array. Very little plastic deformation occurred, and the results were consistent with each other.

Mathematical models developed by Pehrson et al. [29] can be used to predict motion for idealized LET joint array systems.

Two mechanisms—the split-tube flexure and bi-stable switch—were fabricated to see how principles learned from the three simple mechanisms could be implemented to form more complex shapes. While the force–deflection relationship was not measured, these mechanisms still exhibit repeatable and expected behavior for such systems.

Split-tube flexures allow for torsional motion while keeping its shape in both compression and bending [36]. The laser folded segments of the tube starting from the outside and working inward. At one end of the tube, a panel was folded up to act as a handle for actuation. As can be seen in Fig. 12(a), the cylindrical shape was achieved.

To prove repeatability, the mechanism was actuated by hand as shown in Fig. 12(b). The tube was able to be twisted both to the right and the left, demonstrating desirable behavior.

Analytical models shown by Howell [11] for this kind of mechanism can be used to predict motion for idealized split-tube flexures and do not take into account the unique attributes that laser-formed mechanisms have. Although the method shown for achieving curvature for this mechanism accomplishes the desired function, smoother gradients in the shaping could be achieved with laser forming as demonstrated by Cheng and Yao [37].

Bi-stable switches can move between two stable states of the mechanism, and the flexures allow for the mechanism to move between those states [38]. Such switches can be used in complex configurations [39]. Using flexures designed similarly to those in the parallel-guided mechanism and cross-axis flexural pivot, the bi-stable switch demonstrates that the method of laser forming can be expanded for mechanisms with a variety of behaviors. The flexible members were folded up perpendicular to the plane in a way similar to previous mechanisms shown for the forces to not be distributed through the creases, but rather through the flexures. Figure 13(a) shows the implementation of these techniques in a laser-formed bi-stable switch. This mechanism could be integrated with an independent contact to enable a bi-stable electrical switch.

While the mechanism was able to achieve repeated actuation between the bi-stable states, significant plastic deformation occurred to accommodate the motion shown in Fig. 13(b). This contrasts with the other four shown, as they did not experience significant plastic deformation while tested. The increased deformation is likely due to the combined axial and bending loads applied to the compliant beams in the bi-stable switch, while the parallel-guided mechanism and the cross-axis flexural pivot only experienced bending loads.

The design for this mechanism was inspired by principles demonstrated by Opdahl et al. [32] and Zirbel et al. [38]. The models they developed can be used to compute force–deflection relationships for idealized versions of bi-stable mechanisms.

The mechanisms developed performed desirably, as the repeated motion was achieved for all five mechanisms, with force and deflection able to be measured for the parallel-guided mechanism, the cross-axis flexural pivot, and the LET joint array. There are several key challenges with this technology: (1) designs are limited to being formed out of a single sheet, necessitating careful orientation of features, (2) intended forces must take care to not apply undue stress to the laser-formed creases, and (3) the laser can cause warping while cutting because of its high thermal output.

At the moment, the single-sheet design constraint proves difficult to work around for anything more than simple mechanisms. However, multiple sheets could be laser-formed and joined together (via welding, adhesive, locking, etc.) to create more complex, multiple-degrees-of-freedom mechanisms. While many modern rapid prototyping methods use an additive manufacturing process, the laser forming method is subtractive; care must be taken in designing compliant mechanisms so that they can be “subtracted” out of a single sheet. Applying principles of orientation shown in this work allows the ability for both rigid and compliant features to be formed out of a workpiece of a single thickness.

The laser-formed creases are inherently weaker than the rest of the sheet, as the metal has been heated and cooled repeatedly [40]. Designs must be designed to limit forces and stresses distributed through any of the creases. Postprocessing thermal treatment such as annealing could be used to regain any material hardening at the fold.

Thermal factors must be considered when creating laser-formed compliant mechanisms, as the laser will heat up the metal in different ways depending on the laser power, laser speed, repeated passes, and metal used. If more heat is applied to the workpiece than can be dissipated, then the metal will warp to accommodate the added heat [41]. This warpage can prevent the laser from cutting or forming if the warped section of the workpiece is no longer in the focal range of the laser. Even if the laser can successfully cut and form the workpiece, the resulting mechanism may not function as desired because the flexures or rigid sections could be too warped to behave as intended.

Analytical models of the laser-formed mechanisms using pseudo-rigid-body models [11] show discrepancies with the experimental test results. The models show similar trends but were not predictive with linear, isotropic material properties. The deviation was likely due to a variation in material modulus in the heat-affected regions and the compliant boundary condition at the fixed supports in the experimental data. A deeper understanding of the change in material properties should be gained in future work to improve the model predictions. The thermal factors associated with the laser-forming process are likely why the models in their current form are not sufficient for laser-formed compliant mechanisms.

The analytical models show trends but are not a match with the measured behaviors likely due to changes in the thin sheet metal induced by the high heat of the laser. Because this warrants a much more thorough exploration, it can be further analyzed in the future work.

The building-block features of laser-formed compliant mechanisms can be implemented in a variety of ways, with each other and with other rigid components. The rigid and flexible features developed for the parallel-guided mechanism, for instance, can be rearranged into a binary switching concept mechanism as shown in Fig. 14 similar to those developed by Kuppens et al. [39]. This laser-formed version binary switch demonstrates how the rigid features can be created around the edge of the mechanism by reorienting the panels and how the flexible features can be oriented by laser forming and then deformed through mechanical actuation. By having such a compliant switch fabricated out of metal, new functionality can be introduced to the system such as thermal or electrical conductivity.

Laser forming of compliant mechanisms could be useful when manufacturing in locations with limited machinery, as laser metal cutters/engravers can be relatively affordable and compact. Being able to prototype or create replacements for complex metal systems can be a boon in a variety of situations, such as in the field, at a research lab, or at any kind of company where small, metal, compliant components could be useful. As a rapid prototyping method, the techniques presented have the ability to be an accurate and cost-effective solution.

Other applications could include small tunable antennas, locking mechanisms, and large-scale approximations of microelectromechanical systems. The space for applications is vast, with a variety of practical uses.

The fields of laser forming and compliant mechanisms have been successfully joined with the demonstration of five compliant mechanisms cut and formed using only a laser. This research demonstrates that compliant mechanisms can be laser formed and exhibit desirable, repeatable behavior. Simple flexures can be laser formed, oriented, and combined in more complex shapes to achieve a variety of force–displacement behaviors. Five compliant mechanisms were cut and formed, and the techniques for designing such mechanisms were explored. The ability to create compliant mechanisms out of thin sheet metal can be useful in replacing polymer components of similar size because of the unique properties of metal. Also, such mechanisms could be faster to fabricate with laser forming than with traditional methods.

The next step is to implement the principles of this research in designing and fabricating increasingly complex mechanisms with real-life applications. Different types of metals could be explored, like spring steel, brass, and aluminum. Further analytical modeling can be done to predict the behavior of laser-formed mechanisms.

Funding support was provided by the Army Research Lab (ARL), Oak Ridge Associated Universities (ORAU) Journeyman Fellowship program, and the Brigham Young University Mechanical Engineering Department. Various experimental tests and respective data collection performed by Jared Hunter and David Chin at Brigham Young University.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.