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The design goals for the snake robot included
maximum torque-to-weight to allow cantilever support of the snake;
minimum envelope diameter to fit through small openings; minimum
achievable radius of curvature, resulting from short links with
maximum angular travel between links; and rugged construction. Secondary
goals included minimum backlash and compliance in the structure;
and "reasonable" speed of motion. From the outset, a modular
design with all links identical was chosen for simplicity of design,
fabrication and assembly. This is sub optimal in the sense that
the joints near the fixed end of the snake will generally have much
higher loads than those near the ends. Six was chosen as a reasonable
number of joints for the snake, although the real manipulation capabilities
depend also on the degree of travel in each joint.
An actuated universal-joint (U-joint) design
was selected for its simplicity and ruggedness. In this design,
U-joint "crosses" are connected to one link with a pitch
pivot joint, and to the next with a yaw pivot joint. The pitch and
yaw joints are always orthogonal, and intersect along the link centerlines;
this leads to simple kinematics. The pitch and yaw joints are actuated
by linear actuators in the two links. Links are configured such
that the axes at each end of any link are parallel; thus, one link
will have pitch joints at both ends actuated by its two linear actuators;
the next link will have two yaw joints. This arrangement facilitates
packaging of the two linear actuators side-by-side in the link.
Ball screws were chosen for the linear actuators because of their
high efficiency (compared to lead
screws) and effective speed reduction. The screws are fixed in bearings
mounted to the links, while the nuts drive clevises connected to
the crosses of the U-joints. The screws are driven by brush-type,
permanent-magnet, DC motors which can be operated with simple, pulse-width-modulated
(PWM) electronics. For compactness, the gearmotor and ball screw
are placed side-by-side with a small toothed-belt drive connecting
them. Each actuator is mounted to the link through a steel flexure
that accommodated the slight lateral movement of the screw as the
joint angle changes.
A novel feature of this design is the overload
mechanism or "snubber." It is designed to absorb the kinetic
energy of the links and motors when the mechanical stops are reached,
and to accommodate imposed loads on the snake without damage to
the actuators or structure. Belleville spring washers--4 series
sets of 3 parallel-stacked washers--are mounted in the "snubber
housing" such that the ball screw can move axially by 1mm if
the preload value is exceeded. The thrust load of the screw is taken
by a custom-made, 4-point-contact bearing that is integrated into
the snubber housing.
Each link is 41.7mm in diameter, 96.0mm long
(pivot-to-pivot), and weighs about 240g. The ball screws are 6mm
diameter with 1mm lead, are rated at 700N, and are connected to
the crosses at 14.7mm from the pivot. Motors are Maxon RE-13 (13mm
diameter) gearmotors with 16.58:1 planetary gear reducers and 16-count
encoders (64 counts per revolution with quadruature decoding). These
develop about 38mNm of continuous torque; this translates to 380N
of force at the ball screw (well below the rated load), considering
the 2:1 belt drive and transmission efficiencies. The snubber mechanisms
are preloaded to about 600N to protect the ball screws and bearings
from overload; no displacement occurs until this load value is reached,
so the normal stiffness of the structure is not compromised. Motor
no-load speed at the nominal 12V input is 8900RPM, which corresponds
to 5s time to travel the full 22.4mm of screw travel. Joint angular
travel is about +/-55 degrees.
Tests of the joints showed that the actuators
can produce 4.5Nm of torque at 12VDC (0.40A). That is, each ball
screw produces 307N at 14.7mm radius on the U-joint cross. Based
on the expected 5.08mNm at 0.40A, theoretical output would be 1060N
with 100% transmission efficiency. This indicates that overall drive
efficiency is only
(307N/1060N) 29%, much lower than predicted (48%). We will investigate
this to see if significant increases in efficiency and output torque
are possible.
The torque about a joint needed to "cantilever-lift"
(lift when extended
horizontally) a single joint, assuming its center-of-mass (COM)
to be at its geometric center, is 0.113Nm. The torque to lift n
joints is n-squared times this. Given 4.5Nm available joint torque,
the snake should then be able to cantilever-lift 6 joints. Tests
on the complete snake robot confirm this capability. This ability
is important to allow the snake to achieve arbitrary configurations
working against gravity.
At present we have a 7-link, 14-actuator
snake assembled and working. The U-joint cross at one end is mounted
to a fixed base. Joint actuators are individually controlled by
14 switches, allowing the snake to be moved into arbitrary configurations.
Ultimately we need to have the snake under computer control so that
the tip can be moved to the desired position and orientation while
the body of the snake obeys constraints of the environment, etc.
To this end, we are developing and electronics "bus" system
that will carry power and signals between the actuators and sensors
on the snake to a control computer. Hard wiring to all 14 actuators
and encoders would require (14 x 8) 112 conductors and was deemed
unfeasible. The plan is to use an I-squared-C bus on the snake to
connect microcontrollers on the actuators to the control computer.
The technology is available, but packaging the required components
(H-bridge, decoder chip, PIC microcontroller plus passive components)
to fit within the link envelope, and providing interconnects between
controllers, are challenging problems. At present the concept is
to use one PC board per actuator, and have these mounted on each
side of the U-joint crosses; a preliminary look suggests that the
components may barely fit in the space available.
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