Figure 1 shows a metamorphic origami unit with mobility multi-furcation. The origami unit comprised 4 facets and 4 creases. In the folded configuration [(i) in Fig. 1A], the unit could be unfolded around the contiguous creases C2 and C4; in this configuration, creases C1 and C3 are neither contiguous nor collinear. When the unit begins to unfold [(ii) in Fig. 1A], it would, at a certain point, reach a unique intermediate configuration in which creases C1 and C3 are collinear [(iii) in Fig. 1A]. This configuration is the first metamorphic configuration of the origami unit. In this metamorphic configuration, the origami has a mobility bifurcation, such that the origami could continue to unfold around the contiguous creases C2 and C4 or unfold around the new collinear creases C1 and C3. If the origami was unfolded around the collinear creases C1 and C3, then the creases C2 and C4 would no longer be contiguous, thereby preventing the origami unit from being rotated around creases C2 and C4 again [(iv) in Fig. 1A]. The origami is incapable of sustaining load as it is possible to rotate it around creases C1 and C3 [(i) in Fig. 1B]. The unit then continues to unfold to another special intermediate configuration in which creases C2 and C4 are also collinear. This configuration is the second metamorphic configuration of the origami [(v) in Fig. 1A]. In the metamorphic configuration 2, the origami also has a mobility bifurcation. When the origami is rotated around the collinear creases C2 and C4, it moves into another motion pattern until the creases C1 and C3 are no longer collinear [(vi) in Fig. 1A]. After that, the origami would not rotate around creases C1 and C3 again, i.e., the rotation around creases C1 and C3 would be locked. In other words, origami has load-bearing ability in this configuration [(ii) in Fig. 1B and Movie S1]. The metamorphic origami unit with 4 facets and 4 creases was evaluated quantitatively using the ABAQUS software. The simulation process is illustrated in Note S2. Figure 1C illustrates the stiffness of the metamorphic origami unit when the origami unit was folded around the collinear creases C2 and C4 from the metamorphic configuration. The stiffness was observed to increase as the folding angle was decreased. This property demonstrates that, in the metamorphic configuration, the stiffness is close to zero, which enables the origami unit to be folded around the collinear creases C1 and C3. If the origami unit is folded around another set of collinear creases C2 and C4, the creases C1 and C3 no longer remain collinear, and the stiffness is increased further. This implies that the origami unit would no longer be folded around creases C1 and C3 again, i.e., the origami unit has force sustainability. In addition, it was demonstrated that, as the elastic modulus of the origami unit's facet panels increased, the origami unit's stiffness also increased (Fig. 1D). Therefore, a facet with an adequate modulus of elasticity had to be designed if large stiffness was required.

The inflatable metamorphic unit was designed based on the metamorphic origami unit with 4 facets, and a soft pneumatic chamber was used to drive the inflatable origami unit to move from one movement pattern to another. Figure 2A depicts an inflatable metamorphic origami unit with 8 identity rectangular facets attached to a polyethylene (PE) lay flat tube. The soft chamber of the origami was driven by a monolithic pneumatic actuator. Because the air pressure in the chamber was monotonic increasing, then the air capacity of the chamber is also a monotonic increasing process. The inflatable metamorphic origami is initially folded with 2 sets of contiguous creases [(i) in Fig. 2A], namely, the collinear creases C5 and C6, which are contiguous with the collinear creases C2 and C4, such that the inflatable origami can only be unfolded around these 2 sets of contiguous creases in response to increasing pneumatic pressure [refer to (ii) in Fig. 2A]. The folding angle θ is large in this stage, and the extension angle φ is small; based on the stiffness behavior described in Note S2, the stiffness along the extension motion is weaker than the stiffness along the inflation motion of the chamber; thus, the motion in this stage is extension-dominant. When the inflatable metamorphic origami unit reaches the metamorphic configuration in which the creases C1 (C7) and C3 (C8) are collinear [(iii) in Fig. 2A], the origami will change the motion pattern of unfolding around the creases C2 and C4 to that around the creases C1 (C7) and C3 (C8), e.g., the motion pattern changes from extension-dominant to inflation-dominant. When the air input reaches the maximum capacity of the chamber, the origami stops inflating. The origami chamber inflates to maximum capacity when the rhomboid cross-section of the chamber reaches the maximum area value, e.g., folding angle θ = 90° [(iv) in Fig. 2A]. The equivalent pin-jointed truss frame model was established to show the stiffness behavior of this inflatable metamorphic origami unit during the metamorphic deployment process, which verifies that when this inflatable metamorphic origami unit is at maximum capacity state, i.e., folding angle θ = 90°, it has maximum stiffness (Fig. 2B and Note S3). When the inflatable metamorphic origami unit is at minimum capacity, i.e., the folding angle θ = 0° or θ = 180°, the inflatable metamorphic origami is at 2 metamorphic positions, the stiffness of the inflatable metamorphic origami unit in these 2 states are approximate to 0, and the unit can be rotated around the contiguous creases. A physical prototype was also fabricated to demonstrate the sequential deployment process of the inflatable metamorphic origami unit (Fig. 2C) and the load capacity in the deployed configuration (Fig. 2D). The weight of the unit was 8.5 g. Initially, the unit could be folded around the contiguous creases with no payload-sustaining ability. When the unit was inflated, it could sustain a payload of approximately 400 g, which is around 47 times its weight, without much deformation. When the payload continuously increased beyond this weight, the unit generated evident deformation (800 g) (Movie S2).

The inflatable metamorphic origami developed in the present study is capable of realizing an initial deployment motion followed by a stable load-bearing status and could, therefore, be used for supporting large-scale deployable solar arrays in space applications (Movie S3). A branch unit of the developed metamorphic origami is depicted in Fig. 3A. The branch unit of the metamorphic origami was designed as a soft origami chamber with a rhombic cross-section in the deployed configuration, and all creases in this origami are rigid creases (Note S1). Initially, the branch unit is folded into a compact zigzag-shaped configuration [(i) in Fig. 3A]. In this configuration, the upper lateral creases and the lower lateral creases at the 2 ends of each rigid facet are contiguous, and it is possible to deploy the branch unit around these contiguous creases to generate the first deployment motion in response to the air pressure [(ii) in Fig. 3A]. After the origami continues to deploy into the metamorphic configuration with longitudinal collinear creases [(iii) in Fig. 3A], the upper lateral creases and the lower lateral creases are no longer contiguous as the air pressure continues to increase, causing the rotations around the first set of contiguous creases to be locked [(iv) in Fig. 3A]. Using this branch, the radial deployable metamorphic origami with 4 branch units was developed to support a large deployable planar solar array (Fig. 3B and C). The deployment process of this deployable solar array using the developed metamorphic origami is illustrated in Fig. 3D. This origami reaches a considerably high deploy/fold ratio; the deploy/fold ratio for each branch was approximately 38.8, while the deploy area/fold area ratio for the developed radial deployable metamorphic origami with 4 branches supporting a deployable planar solar array was approximately 20.8.

The metamorphic origami developed in this study can generate sequential unfolding motions around various sets of contiguous/collinear creases, which were characterized by a large initial deployment motion followed by a stable load-bearing status. The creases in this origami could only generate rotational motions for folding/unfolding. Furthermore, due to the flexibility of the soft creases, this origami had a slight thickness accommodation, which is especially important for the folding/unfolding motion of contiguous creases. However, the creases must be precise to maintain load-bearing capability and provide strict geometric constraints to the origami to generate a kinematically guided origami folding, similar to a rigid mechanism. Therefore, this type of origami crease was termed a rigid crease (Note S1).

In order to demonstrate the versatility of the developed metamorphic origami, a circumferential deployable metamorphic origami was developed to support a large deployable curved-surface antenna, which would be able to generate an initial deployment motion of a large magnitude followed by a bending motion for adjusting the curvature of the supporting deployable curved-surface antenna (Movie S4). Similar to radial deployable metamorphic origami, circumferential deployable metamorphic origami also comprises 4 branches. In the initial folded configuration, these branches are folded around the rigid folding contiguous creases that surround a square mounting base [Fig. 4A(i) and Fig. S6H]. In response to increasing air pressure, the branch first deploys into an unbent status [(ii) in Fig. 4A], which is a metamorphic configuration with 4 longitudinal collinear creases. Next, the branch continues to inflate around the 4 longitudinal collinear creases in response to the air pressure until it reaches the second metamorphic configuration in which the cross-section of the branch becomes triangular [(iii) in Fig. 4A]. In this configuration, the creases for the initial deployment are no longer contiguous, causing the unfolding around these creases to be locked. In the second metamorphic configuration, the origami reaches new lateral collinear creases, enabling the branch to be unfolded around the lateral collinear creases as the air pressure increases. In order to realize the bending motion around the lateral collinear creases, the design used stretchable creases, capable of generating both folding/unfolding motion and stretching motion owing to their wrinkled structure. Different from what was reported in a previous study [13], this stretching motion realized in the present study was not due to the stretching of the soft body and rather due to the stretching motion of the wrinkled structure (Note S1). In the first deployment motion, this metamorphic origami branch was deployed around the rigid creases, similar to a rigid mechanism. The stretchable creases provided adaptive accommodation motion without introducing kinematic constraints, and this was termed a rigid-dominant motion. When the branch was moved to the metamorphic configuration 2 [(iii) in Fig. 4A], it could be unfolded around the lateral collinear creases to generate a bending motion. In this process, the lateral collinear creases worked as rigid folding creases, which ensured the kinematic constraints and precise motion. On the other hand, the stretchable creases worked in the stretching motion to provide the bending actuation force. The bending motion of the origami branch was, therefore, a superimposition of the rigid geometry-driven motion generated by rigid creases and the stretching motion generated from the stretchable creases [(iv) in Fig. 4A and Note S1]. The bending motion of this origami was, therefore, termed the rigid-flexible coupling motion. This branch was used for developing a circumferential deployable metamorphic origami with 4 branch units to support a large deployable curved-surface antenna (Fig. 4B and C). The deployment process of the deployable curved-surface antenna driven by this metamorphic origami is illustrated in Fig. 4D. The circumferential deployable metamorphic origami reached a considerably high deploy/fold ratio of 29.1 for the prototype developed in the present study.

The developed circumferential deployable metamorphic origami exhibited sequential motion patterns under a single pneumatic actuation that could be applied to soft deployable robotic systems. Two types of deployable metamorphic origami graspers were developed in the present study to demonstrate the potential versatile applications. The first type of grasper was a multi-fingered deployable grasper. The architecture of this multi-fingered metamorphic origami grasper was similar to that of the circumferential deployable metamorphic origami, which could generate sequential deployment motions to realize a large working space motion and a bending motion for grasping large-sized objects. Initially, the branch is folded into a zigzag-shaped configuration [(i) in Fig. 5A]. As the air pressure increased, the branch was first deployed into an unbend configuration around the contiguous creases (rigid-dominant), which was followed by a motion in which the branch reached the first unbend metamorphic configuration with 6 longitudinal collinear creases [(iii) in Fig. 5A]. Subsequently, the origami continued to inflate to the second metamorphic configuration with a rectangular cross-section by unfolding around these longitudinal collinear creases [(iv) in Fig. 5A]; this process was also termed a rigid-dominant process. In the second metamorphic configuration, the creases for the initial deployment [(ii) in Fig. 5A] no longer remained contiguous, causing the unfolding around these creases to be locked. With the continuous increase in the air pressure, the stretchable creases begin working, thereby generating a bending motion for grasping large -sized objects [(v) in Fig. 5A]. This bending motion process is a rigid-flexible coupling motion process generated by both rigid creases and stretchable creases. This branch was then used for developing a triple-fingered deployable grasper for grasping large -sized objects (Fig. 5B and C). Next, to demonstrate the size adaptability of this metamorphic origami grasper in grasping large -sized objects, grasping experiments were conducted (Movie S5). The entire grasping process of this grasper based on metamorphic origami is illustrated in Fig. 5D. The grasper was observed to be capable of grasping objects 3 times its size.

The second type of grasper was the leaf-shaped deployable grasper, which had branches with a vegetal leaf-shaped structure. The grasper comprised 3 leaf-shaped branches, which could generate an enveloping motion for grasping heavy objects (Fig. 6B). Initially, the branches are folded around a mounting base [(i) in Fig. 6A and Fig. S8G]. The branches could then be deployed around the longitudinal contiguous creases circumferentially into the first metamorphic configuration [(i) and (ii) in Fig. 6A]. Afterward, the branches could be continued to be deployed around another set of lateral contiguous and collinear creases [(iii) in Fig. 6A] to the second metamorphic configuration [(iv) in Fig. 6A]. In the second metamorphic configuration, a new longitudinal collinear crease was reached, which enabled the generation of a slight folding motion of the origami around this collinear crease; combined with bending motion, these 2 motions achieve envelope grasping together [(v) in Fig. 6A]. This branch was then used for developing a deployable grasper for grasping heavy objects (Fig. 6B to D). The diameter of the grasper in folded configuration was 8 cm. The diameter of the object was approximately 16 cm, which is 2 times that of the grasper in the folded configuration. The total weight of the 3 branches was 45 g, while the grasper could grasp an object weighing up to 377.3 g, which is 8.3 times the weight of the grasper (Movie S6).

The flexible PE lay flat tubes (thickness: 0.1 mm) were used for fabricating the pneumatic inflatable soft origami chambers. The carbon fiber sheets (thickness: 0.4 mm for the radial and circumferential deployable metamorphic origami and 0.3 mm for the multi-fingered deployable metamorphic origami grasper) and the flexible polyvinyl chloride sheets (thickness: 0.5 mm for the leaf-shaped deployable metamorphic origami) were used for fabricating the rigid facets of the metamorphic origami. The mounting bases of the metamorphic origami were fabricated using high-toughness photosensitive resin through 3D printing technology.

The rigid facets were attached to the flexible PE lay flat tubes to obtain the creases of the metamorphic origami between the adjacent facets. The metamorphic origami was fabricated according to the following rules:

1. Kapton double-sided sticky tapes (0.1 mm thick) were used to attach the rigid facets to the inflatable soft PE lay flat tubes (Fig. S4A).

2. The terminal of the PE lay flat tube was sealed using a heat sealer (PFS-300; Baijie Ltd.) to form the pneumatic chambers for each branch (Fig. S4B).

3. In order to realize the metamorphic origami with both deployment motion and bending motion, the stretchable creases were first squeezed to form wrinkles with the same gap as that in the rigid creases. The rigid creases responsible for the geometric folding/unfolding were glued using the 3M610–1PK tape (Scotch; 3M Ltd.) to ensure their non-stretchability; consequently, these rigid creases could generate pure folding/unfolding motion (Fig. S4C). The stretchable creases owed their stretchability and foldability to the wrinkled structure, which provided space for the bending motion. The bending motion could then be generated through the folding/unfolding motion of the rigid creases combined with the stretching motion of the stretchable creases.

4. In order to obtain the rigid creases of the radial deployable metamorphic origami, the outer surface of the facets was glued using the 3M610–1PK tape (Scotch; 3M Ltd.) to render it non-stretchable (Fig. S4C). This also improved the stiffness of the origami.

5. The non-sealed ends of the origami branches were glued on the mounting interfaces of the base using double-sided sticky tape (Fig. S4D).

6. Sil-Poxy silicone adhesive (Smooth-On Inc.) was also used to seal the mounting interfaces of all branches to produce a deployable metamorphic origami with adequate airtightness (Fig. S4E).

All deployable metamorphic origami designed in the present study were controlled using a pneumatic source system. Each deployable metamorphic origami was actuated using a single pneumatic source through a soft polyurethane tube. The air pressure was controlled using a servo valve.

The stiffness simulations were performed using the commercially available FEA software named ABAQUS (Dassault System). Rectangular rigid panels were attached to a soft membrane to establish the origami simulation model. The rigid facets were formed using an acrylic plate material, while the membrane was formed of paper material. The elastic modulus values of the rigid facets and the soft membrane were set to 3,300 MPa and 0.5 MPa, respectively, while the Poisson ratio for both rigid facets and the soft membrane was set to 0.2. Consequently, the crease could be obtained between the 2 adjacent rigid panels due to the difference between the stiffness of the rigid panels and that of the membrane (Fig. S2B and Note S2). In order to perform the stiffness simulation, the 2 edges of the facets of the metamorphic origami unit were fixed, and 2 identical loading forces were applied to the 2 edges of the other 2 facets opposite to the fixed ends. The loads were applied along the direction of the bisector of the folding angle (Fig. S2D). The stiffness of a point was calculated by measuring the displacement of the force loading point along the direction of the loads (Note S2). The stiffness behavior of the inflatable metamorphic origami unit was analyzed by establishing the equivalent pin-jointed truss frame model (Note S3).