Stephen Hagberg

Journal of Undergraduate Research
Volume 5, Issue 1 - October 2003

Design and Construction of a Proof of Concept Prototype for a Six-Degree of Freedom Hexapod Motion Nano-Positioning Device

ABSTRACT

In the field of photonics the need for a device capable of motion in six-degrees of freedom with a resolution on the order on nanometers is growing. Fueled by increasing standards of precision in fiber optic cable alignment as well as the need for higher throughput on manufacturing lines opens the problem to new approaches in kinematics and motion control. Using a device based on a six-degree of freedom Stewart platform or hexapod geometry, a proof of concept device was constructed to determine if such an approach can prove to be a cost effective way of solving the problem. The main driving forces in the design are to devise a scheme that lends itself well to computer automation while finding more cost effective solutions to many of the design factors and components involved. This report will focus on the design and construction phase of the project.

INTRODUCTION

In the field of photonics the need for a more cost effective and automated process for aligning a diode laser with a fiber-optic cable is increasing. This alignment process requires a device capable of a full range of motion with the ability to create and resolve as small movements as mechanically possible accurately and repeatedly. Currently the vast majority of devices on the market are very expensive and by virtue of their designs do not lend themselves well to computer controlled automation. The increasing trend towards automation can be seen in virtually all fields of manufacturing and with the exponential rise in the application of fiber-optic technologies companies are focusing on new ways to streamline their manufacturing processes, specifically the alignment phase, in hopes of keeping up with demand while at the same time lowering the cost of their product.

Dr. John Ziegert, professor of Mechanical Engineering at the University of Florida, has found a novel approach for addressing the problem of automation while at the same time allowing for a significant cost reduction in the construction of such a device. The idea or concept is based upon a method of translating a rotational motion into a vertical one. By merging this concept with existing structures in kinematics a device can be conceived which has the capability of producing the desired ranges of motion and resolution necessary for fiber-optic cable alignment.

The purpose of this research is to design and construct a working prototype to test the functionality of Dr. Ziegert’s idea. The goal is to determine through experiment the fundamental resolution for this device and compare it to figures calculated from the kinematics of the design. This report will be limited to the design phase only. Primarily this includes the determination of key design parameters as well as the selection of all materials and components necessary for construction of the prototype.

DESIGN CRITERIA AND REQUIREMENTS

A fiber-optic cable is a thin glass fiber that transmits a signal though a series of high and low pulses of light from a semiconductor laser affixed to one end of the fiber. Because the diameter of a fiber can often be as small as 5 micrometers¹ any alignment or positioning must take place at sub-micron levels [1]. For example, in order to accurately align such a fiber would require positional accuracy of 50 nanometers² [2]. This is no easy task considering the thickness of a sheet of paper would need to be divided approximately 10,000 times to produce 8 nm segments.

Furthermore, to mechanically align any two objects in free space requires a full range of motion commonly referred to as six-degrees of freedom, three linear and three angular. The linear motions are merely translations either from front-back, up-down, and left to right, while the angular components of motion are rotations about each of these directions, roll, yaw, and pitch. Therefore the position and orientation of one object relative to another can be completely described by decomposing its coordinates into these six components or degrees of freedom.

Thus a suitable device must be able to create accurate and repeatable motion in six-degrees of freedom on the order of nanometers, while also keeping cost and ease of automation in mind as well.

BASIC CONCEPT

The Historically, the way to go about creating six-degree of freedom motion has been to control each axis or component of motion independently from each other. This type of Cartesian motion has been predominately used for positioning devices for a multitude of reasons. However such devices tend to become large and cumbersome due to the requirement that individual axes must carry subsequent axes in the serial kinematic chain. Since any change in position of one axis may affect the alignment of another axis a process of cycling through each axis of motion may be required to reach a final optimum alignment location. This problem has stimulated much interest in areas of motion control and kinematics, particularly parallel kinematics, where a variety of devices have been studied.

The field of parallel kinematics owes its uniqueness to the unconventional way in which motion is created. Of particular interest is a device commonly referred to as a “Stewart Platform” or hexapod which creates six-degree of freedom motion of a platform by varying the lengths of the six legs or struts which support it thereby allowing it to tilt and move in various directions [3]. With advances in computing technology the motion created by a hexapod, while seemingly unnatural and difficult to express analytically, can be controlled to produce the fundamental Cartesian type displacements while allowing for rather complex motions as well.

Therefore the design geometry will be based off that of a hexapod structure, however the uniqueness of Dr. Ziegert’s idea lies in how the legs will actuate this tilting motion of the platform. The idea is to convert a rotational motion into one which can cause movement of the platform. This is done by means of a cylinder capable of rotation which is connected to the platform by a strut of fixed length with spherical joints at both of its ends. So while the geometry resembles that of a standard hexapod, it differs by way of having fixed length legs whose lower joints move in a circular motion caused by the rotary actuators (figure 1).

Figure 1. Design Concept for Six-Degress of Freedom Motion.

Furthermore, to test the fundamental resolution of the device only one cylinder need be actuated while the others can be held fixed. Therefore the device to be created will fully resemble the six-degree of freedom machine, however, only one degree of freedom will be tested in the proof of concept prototype described here. By successfully demonstrating the capability of this approach in one degree of freedom the concept can be extended by allowing all six cylinders to rotate thereby creating the six degree of freedom configuration required.

DETERMINATION OF DESIGN PARAMETERS

The key parameters of this design are the locations of the spherical joint centers on the base and platform as well as the length of the struts. To greatly simplify the analysis a two-dimensional model will be used to determine some “ballpark” parameters for the design. Consider the movable platform to be a simple beam allowed to pivot at one end with the other connected by a spherical joint to a leg of fixed length which connects to the actuator (figure 2). Then one can see that the beam deflects from its maximum to minimum height in half the rotation of the cylinder or 180 degrees.

Figure 2. Two Dimensional Model Height Deflections with Actuator Rotation.

This change in height of the endpoint of the beam with angular rotation of the cylinder is what we are interested in determining. Also the fact that this height change occurs for 180 degrees of rotation has a direct effect on the range and resolution; both of which are important driving factors in the design. To express this problem analytically consider the 2-D model with the dimensional variables indicated below (figure 3).

Figure 3. Two Dimensional Model Design Variables.

These variables indicate the joint locations on the platform and base as well as the length of the strut. Using these to obtain an expression for the change in height ΔZ, which equals the maximum height minus the minimum height, one finds:

Hence values for L, S and R can be determined which produce a given ΔZ. A spreadsheet approach to the analysis of these parameters was conducted. Care was taken to avoid singularities and points where a small change in one of the variables would lead to a large change inΔZ. This sensitivity associated with each variable is important with regards to manufacturing tolerances for the construction of the device.

Furthermore, the way in which the height of this beam changes with rotation of the cylinder is non-linear, in fact it is sinusoidal (figure 4). This sinusoidal relationship is a result of the circular motion in which the lower joint undergoes. Because of this non-linearity between the controlled input, angular rotation, and the desired output, change in height, testing will be done at the most sensitive position or half way point.

Figure 4. Plot of Height vs. Angular Rotation of Actuator.

While this two dimensional analysis is to some degree an over simplification of the motion, its use is justified because it provides quite a bit of useful information regarding the geometry and behavior of the design sketched in figure 1.

COMPONENT SELECTION AND CONSTRUCTION

When building anything the components available often dictate the design. This is most apparent here by the way in which the range and resolution is determined by how small an increment of rotation can be created. Therefore having a high quality angular position indicator, more commonly referred to as a rotary encoder, will be very important. Furthermore, other key components in the design are the motor and bearing used for the actuator as well as the spherical joints at both ends of the legs.

Rotary Encoder
The key factor here is the number of counts per revolution (CPR). For example, an encoder with two million CPR would have one million counts over the range of motion ΔZ. Now if ΔZ was set equal to 2 mm then the range of motion could theoretically be divided into one million 2 nanometer segments. Therefore the encoder performance is directly tied to the range and resolution of the device. The encoder used in this design is from MicroE Systems and has the capability of 2.56 million CPR [4].

Motor and Bearing Configuration
The motor used must also be able to create the small movements reliably and accurately. Borrowing on technology perfected and mass produced in the computer hard drive industry it was decided to use a rotary voice coil actuator to provide the rotation of the cylinder. By virtue of their design these actuators can produce extremely fine resolution, limited only by the feedback device which closes the control feedback loop, in our case the encoder. Furthermore, an air-bearing from New Way Machine Components Inc. will be used to provide the smooth and low friction rotation required.

Spherical Joints
The spherical joints for this prototype utilize three steel balls arranged in an equilateral triangle pattern such that another steel ball attached to a strut can rest in them. Each joint consists of three 1/8” balls and one 3/16” steel ball and to help with the assembly of the hexapod structure the 3/16” balls at the ends of the legs are magnetized. This configuration while not as stable as typical ball and socket type joints provides for smooth and low friction motion required for precise positioning and can be seen pictured below as part of the fully assembled prototype (figure 5).

Figure 5. Fully Assembled Prototype.

CONCLUSIONS

With the need for a for a more automated and precise device for photonic assembly systems a great deal of research has been conducted in the field of parallel kinematic structures. Using a modified hexapod geometry a proof of concept prototype for a six degree of freedom nano-positioning device was constructed. The objective was to determine by experiment the smallest increment of motion that can be created accurately and repeatedly. Design parameters and the behavior of its motion were approximated using a two dimensional model. Additionally, the primary components in the design were presented and discussed. Ensuring that these key components are integrated properly into the design of the prototype is instrumental in being able to gain accurate and useful data from it. Ultimately, demonstrating the possibility of using a more cost effective approach which allows for higher throughput in fiber-optic cable assembly would alleviate a growing demand from industry. If successful such a device would increase production in the fiber optic industry therefore creating lower costs and brooding the list of potential applications.

FOOTNOTES

One micrometer or micron (um ) is equal to 10^-6 meters or 0.00003937 inch.
One nanometer (nm) is equal to 10^-9 meters or 0.00000003937 inch.

REFERENCES

Callister W D 2000 Materials Science and Engineering: An Introduction 5th ed. John Wiley & Sons, Inc. pp 726
Weber A 2001 Positioning for Fiber Optics Assembly. Assembly Magazine May
Stewart D 1965 A Platform with Six Degrees of Freedom. Proc. Inst. Mech. Engr. 180(1):371-386
MicroE Systems Mercury 3000 series Encoders www.microesys.com

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