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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. |
