Extendable arm, variable shape frame, and variable shape three-dimensional structure

1. An extendable arm, comprising:

a plurality of cross units arranged in one direction with adjacent cross units of the plurality of cross units being pivotally coupled via end coupling shafts, each cross unit of the plurality of cross units comprising:

a first rigid member having an engaging protrusion extending away from an outer surface of the first rigid member; and

a second rigid member crossing the first rigid member in an X shape and pivotally coupled with the first rigid member via a middle coupling shaft, the second rigid member comprising an engaging recess configured to receive the engaging protrusion such that the engaging protrusion and the engaging recess, which move toward each other as the extendable arm extends, fit together when the extendable arm extends to a predetermined length,

wherein the engaging recess extends into a body of the second rigid member.

2. The extendable arm according to claim 1 , wherein

the engaging protrusion extending away from the outer surface of the first rigid member of least one cross unit of the plurality of cross units is between an end of the first rigid member of the least one cross unit and a midpoint of the first rigid member of the least one cross unit, and

the engaging recess extending into the body of the second rigid member of the least one cross unit is between an end of the second rigid member of the least one cross unit and a midpoint of the second rigid member of the least one cross unit.

3. A variable shape frame, comprising the extendable arm of claim 1 , wherein the extendable arm is a first extendable arm, and the variable shape frame further comprises:

a second extendable arm;

a third extendable arm; and

a fourth extendable arm,

wherein

the first extendable arm is coupled with the third extendable arm and the fourth extendable arm,

the second extendable arm is coupled with the third extendable arm and the fourth extendable arm, and

a starting end of each of the first extendable arm, the second extendable arm, the third extendable arm, and the fourth extendable arm is pivotally coupled with a terminal end of an adjacent one of the first extendable arm, the second extendable arm, the third extendable arm, and the fourth extendable arm via one or more of the end coupling shafts.

4. The variable shape frame according to claim 3 , wherein

the first extendable arm and the second extendable arm are linear arms that are parallel to each other and extend and collapse in a linear fashion,

the third extendable arm and the fourth extendable arm are semicircular arms that extend and collapse in a curved fashion,

the third extendable arm and the fourth extendable arm have opposing 180-degree semicircular shapes when in an extended state, and

the variable shape frame is an obround-shaped frame.

5. A variable shape three-dimensional structure, comprising the variable shape frame according to claim 3 , wherein the variable shape frame is a first variable shape frame, and the variable shape three-dimensional structure further comprises:

a second variable shape frame arranged at an interval in a vertical direction away from the first variable shape frame; and

at least one a longitudinal coupling member connecting the first variable shape frame and the second variable shape frame.

6. The variable shape three-dimensional structure according to claim 5 , wherein the at least one longitudinal coupling member comprises a plurality of longitudinal coupling members, and the variable shape three-dimensional structure further comprises:

an enclosing member that weaves around adjacent longitudinal coupling members of the plurality of longitudinal coupling members,

wherein the enclosing member is on an outside of alternating longitudinal coupling members of the plurality of longitudinal coupling members and on an inside of longitudinal coupling members of the plurality of longitudinal coupling members between the alternating longitudinal coupling members such that the enclosing member closes the interval in the vertical direction between the first variable shape frame and the second variable shape frame so as to enclose at least one of an outer or an inner periphery of the variable shape three-dimensional structure in a direction transverse to the vertical direction.

7. The variable shape three-dimensional structure according to claim 5 , wherein the at least one longitudinal coupling member comprises a plurality of longitudinal coupling members, and the variable shape three-dimensional structure further comprises:

an enclosing member comprising a plurality of panels, each panel of the plurality of panels is coupled with one of the vertical coupling shafts, and each panel of the plurality of panels is coupled with an adjacent panel of the plurality of panels by a middle bend shaft, wherein

the enclosing member is caused to project outwardly away from the plurality of longitudinal coupling members such that the enclosing member is in a zig-zag shape when the variable shape three-dimensional structure is in a collapsed state, and

the enclosing member closes the interval in the vertical direction between the first variable shape frame and the second variable shape frame so as to enclose an outer periphery of the variable shape three-dimensional structure in a direction transverse to the vertical direction.

8. The variable shape three-dimensional structure according to claim 7 , wherein the enclosing member is a first enclosing member comprising a plurality of first panels, and the variable shape three-dimensional structure further comprises:

a second enclosing member comprising a plurality of second panels, each second panel of the plurality of second panels is coupled with one of the vertical coupling shafts, and each second panel of the plurality of second panels is coupled with an adjacent second panel of the plurality of second panels by an inner middle bend shaft,

wherein

the second enclosing member is caused to project inwardly into a space between the plurality of longitudinal coupling members such that the second enclosing member is in a zig-zag shape when the variable shape three-dimensional structure is in the collapsed state, and

the second enclosing member closes the interval in the vertical direction between the first variable shape frame and the second variable shape frame so as to enclose an inner periphery of the variable shape three-dimensional structure in the direction transverse to the vertical direction.

9. The variable shape three-dimensional structure according to claim 5 , wherein the at least one longitudinal coupling member comprises a plurality of longitudinal coupling members, and the variable shape three-dimensional structure further comprises:

an enclosing member comprising a plurality of panels, each panel of the plurality of panels is coupled with one of the vertical coupling shafts, and each panel of the plurality of panels is coupled with an adjacent panel of the plurality of panels by a middle bend shaft, wherein

the enclosing member is caused to project inwardly into a space between the plurality of longitudinal coupling members such that the enclosing member is in a zig-zag shape when the variable shape three-dimensional structure is in a collapsed state, and

the enclosing member closes the interval in the vertical direction between the first variable shape frame and the second variable shape frame so as to enclose an inner periphery of the variable shape three-dimensional structure in a direction transverse to the vertical direction.

10. A variable shape frame, comprising the extendable arm of claim 1 , wherein a starting end of the extendable arm is pivotally coupled with a terminal end of the extendable arm opposite the starting end of the extendable arm via one or more of the end coupling shafts.