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G. K. Ananthasuresh
Fig. 4 A two-axis micro-mirror: a, b top and isometric views of a hexagonal block with two pairs
of torsional hinges compactly arranged to give two-axis gimbal; c two-axis rotation of the mirror;
d serpentine beam serving as a rotational hinge: when it twists, those marked with “u” move out
of the plane and those with “d” move into the plane; and e a simple way to realize the serpentine
beam rotational hinge using a few slits etched in a rectangle
and the other end is connected to a body that is required to rotate, the beams bend
alternately up and down. This is indicated with letters “u” and “d” in Fig. 4d. When
the serpentine beam twists by bending about the axis as shown in Fig. 4e, the beam
segments marked with “u” move up and those with “d” move down. The longer
beam segments deform accordingly, also up and down. A simple way to realize a
serpentine beam in a single layer can be understood from Fig. 4e: We just need
to etch a few narrow rectangular slits. As shown in Fig. 4a, b, such slits can be
etched in a hexagon along with annular slots. The result is an amazing disk at the
center with the capability to rotate about two in-plane orthogonal axes and by large
angles. Once again, the distributed compliant design with bending of slender beams
keeps the stress low. Furthermore, the rotational stiffness of the rotary joint in this
design is quite low. The range of rotation and the rotational stiffness is limited by the
microfabrication process. If lithography permits 1-µm-wide slits, many beams can
be incorporated into the serpentine beam of a given size. However, even with a 5-µmwide slit, substantial range of rotation with sufficiently low stiffness is possible with
this design. Thus, ease of manufacture is a remarkable trait of this design that gives a
rather complex functionality. This design is so simple and elegant that its ingenuity
can be appreciated only if one contemplates alternative designs that surpass this.
G. K. Ananthasuresh
Fig. 4 A two-axis micro-mirror: a, b top and isometric views of a hexagonal block with two pairs
of torsional hinges compactly arranged to give two-axis gimbal; c two-axis rotation of the mirror;
d serpentine beam serving as a rotational hinge: when it twists, those marked with “u” move out
of the plane and those with “d” move into the plane; and e a simple way to realize the serpentine
beam rotational hinge using a few slits etched in a rectangle
and the other end is connected to a body that is required to rotate, the beams bend
alternately up and down. This is indicated with letters “u” and “d” in Fig. 4d. When
the serpentine beam twists by bending about the axis as shown in Fig. 4e, the beam
segments marked with “u” move up and those with “d” move down. The longer
beam segments deform accordingly, also up and down. A simple way to realize a
serpentine beam in a single layer can be understood from Fig. 4e: We just need
to etch a few narrow rectangular slits. As shown in Fig. 4a, b, such slits can be
etched in a hexagon along with annular slots. The result is an amazing disk at the
center with the capability to rotate about two in-plane orthogonal axes and by large
angles. Once again, the distributed compliant design with bending of slender beams
keeps the stress low. Furthermore, the rotational stiffness of the rotary joint in this
design is quite low. The range of rotation and the rotational stiffness is limited by the
microfabrication process. If lithography permits 1-µm-wide slits, many beams can
be incorporated into the serpentine beam of a given size. However, even with a 5-µmwide slit, substantial range of rotation with sufficiently low stiffness is possible with
this design. Thus, ease of manufacture is a remarkable trait of this design that gives a
rather complex functionality. This design is so simple and elegant that its ingenuity
can be appreciated only if one contemplates alternative designs that surpass this.