- Ken Perlin

## Introduction

There are a number of properties we'd like for robotic manipulators, and it is difficult to achieve all of these at the same time:
• no backslip
• direct drive
• rigid construction
• hollow cavity to transport tubing and electrical cables
• light weight
• statically mounted motors
• simple mechanism
• high scalability
I've developed an approach that satisfies all of these constraints. It does this by using a novel drive mechanism, which transmits multiple degrees of freedom of movement through a series of N concentrically arranged hollow tubes. All mechanical movement from each stage is transmitted to succeeding stages via the relative rotation about a common central axis of these tubes, which can also provide mechanical support. The drive power of any given tube is either:
• used to rotate or bend the next stage, or
• transmitted to a system of concentric tubes that forms the next stage
This process is continued in a succession of stages, until all N degrees of freedom have been used.

## The pieces

The mechanism consists of a sequence of joints, connected to one another by limbs each of which is a set of concentric cylinders.

The pieces are:

1. a set of external driving motors,
2. a set of limbs, ie: sets of concentric hollow rigid cylinders,
3. low friction bearings, one between each pair of successive limbs,
4. at each joint, a support structure,
5. mounted on each such support structure, an axle
6. at each joint, a set of no-backslip gears. For each cylinder of the limb preceding the joint which is nested inside some other cylinder, there is a corresponding gear.
Each cylinder that is nested inside another cylinder is slightly longer than the cylinder which surrounds it. This length difference creates a contact area between that nested cylinder and its corresponding gear.

At each joint, there can be two degrees of freedom: a twisting rotation, followed by a bending rotation. These movements are driven by the two outermost cylinders of the limb preceding that joint. For this reason, if any limb contains n concentrically nested cylinders, then the following limb will consist of n-2 concentrically nested cylinders, where each cylinder corresponds to one of the n-2 innermost cylinders of the preceding limb.

If the at its base the mechanism contains N concentrically nested cylinders, then the complete mechanism can consist of N/2 successive limbs, each of which can be rotated with 2 degrees of freedom.

## Internal sequence of operation

At each limb other than the final limb, the outer cylinder rotates the support structure, which in turn causes the axle to rotate about the central axis of that limb. Every cylinder other than the outer cylinder drives one gear.

The outermost nested cylinder (ie: the cylinder nested just inside the outermost cylinder) drives a backdrivable gear which is rigidly connected to a sleeve that surrounds the next limb. When this cylinder rotates, it causes the gear to rotate, which forces the next limb to be rotated about the axle at the joint.

All other successively nested cylinders cause their corresponding gears to rotate, which in turn drives the nested cylinders at the next joint to rotate.

## User's view of operation

The important aspects of this mechanism from the user's point of view are:
• The links are extremely precisely controllable and backdrivable. That is, if force is applied to the end effector, that force is transmitted directly back to the motors. This is not the case with conventional gear links. This means that the finger can manipulate different materials (softer or harder) while applying differing amounts of pressure.

• The motors can all be arranged statically at the base of the mechanism - the driving motors do not need to move. this allows the mechanism to be very stiff and have very low inertia, since the moving parts to not need to bear any motors as part of the load. It also means that more powerful and less expensive motors can be employed, since they do not need to be optimized for low mass.

• The mechanism is hollow. This allows various cables and tubing to pass through the inside of the mechanism to the end effector, if desired.

## An example

In the configuration I'm working on now, the effector has six degrees of freedom, comprised of three stages, each stage effecting two degrees of freedom. We label these degrees of freedom 1a, 1b, 2a, 2b, 3a and 3b, respectively. Each stage effects first a twist about the central axis, followed by a bend perpendicular to the central axis.

The successive stages are joined as nested tubes of progressively smaller radius, 1b being nestable inside 1a, 2a being nestable inside 1b, and so forth. Where each such pair of tubes join they are separated by a low friction rotationally sliding joint. Each such joint can be implemented by a teflon coating, or by an annular ring ball bearing, or by any other standard mechanism for enabling nested tubes to be supported while remaining free to rotate one within the other.

Below is a view of the complete mechanism, color coded as follows:

• Stage 1, effector for turning degree of freedom 1a
• Stage 1, effector for bending degree of freedom 1b
• Stage 2, effector for turning degree of freedom 2a
• Stage 2, effector for bending degree of freedom 2b
• Stage 3, effector for turning degree of freedom 3a
• Stage 3, effector for bending degree of freedom 3b
 Color-coded mechanism (click on the image for VRML animation)

Below is an exploded view of stage 1 and part of stage 2, demonstrating the two degrees of freedom effected by stage 1. The three images on the left are, respectively, these three components. The image on the right shows these components all assembled into the mechanism.

 Exploded-view of one joint (click on the image for VRML animation)

Below is a view of the complete mechanism in gray-scale. Note that light colored parts alternate with dark colored parts. The light colored parts indicate those sections that effect bending about an axis perpendicular to the central axis. The dark colored parts indicate those sections that effect rotation about the central axis.

 Gray-scale view of the complete mechanism (click on the image for VRML animation)

Below are several views of the assembled mechanism.

 Finger with six degrees of freedom (click on the image for VRML animation)

The same finger with 90o rotation for last two degrees of freedom

Close-up of the first joint, in neutral position

Close-up of the first joint, with rotation in second degree of freedom (bending of first joint). Note the twisting in later joints, due to coupled rotation in later degrees of freedom

Close-up of first joint, with rotation in first degree of freedom (twisting at first joint). Note the bending at first joint, due to coupling between the first and second degrees of freedom.