A Virtual Reality Environment for Spherical Mechanism Design

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Overview

This project will result in the development of a virtual environment to facilitate the design of spherical mechanisms. Spatial mechanisms are devices composed of mechanical links and hinged and sliding joints that are designed to produce complex three-dimensional motion. Spherical mechanisms are the simplest class of spatial mechanisms. These mechanisms provide the means to move and orient an object along a complex 3D path. Often today, this type of motion is provided by a series of planar mechanisms. One example is mechanism used to store the folding table attached to a lecture hall seat. This mechanism consists of two independent planar mechanisms that result in fully 3D motion.

Spherical mechanisms are rarely used in industry today because the form and function of these mechanisms is difficult to visualize until a prototype has been built. The geometric complexity of the solution space is beyond the ability of existing systems to present clearly and use fully. The unique 3D nature of the design environment provided by virtual reality is the only vehicle for providing a usable design tool for the design of spatial mechanisms. A computer tool providing a 3D design space where the designer could synthesize spherical mechanisms and obtain a sense of the form and function of the devices while still in a computer modeled form would open up the possibilities for spatial mechanisms to be incorporated into many products including manufacturing equipment and consumer products. The replacement of several planar mechanisms with one spherical mechanisms will result in a solution with fewer links, fewer driving motors, more reliability and lower cost. Providing a virtual environment for spatial mechanism design will not only open new possibilities for invention of new mechanisms, but also will provide new knowledge pertaining to the use of virtual reality as a design tool.

Researchers from the University of California, Irvine, Florida Institute of Technology, and Iowa State University have joined in this proposal to build such a design tool. Preliminary results have shown the need for advancement of spherical mechanism design methodology as well as an evaluation of the suitability of various virtual reality menu structures, interaction devices and display devices to the task of engineering product design.

History

The need for better software to design spherical mechanisms results from the experiences of Professor J. Michael McCarthy, Professor Pierre Larochelle, and Professor Judy Vance.

Four-bar spherical mechanisms are the simplest types of spatial mechanisms and yet even these are difficult to design using existing computer tools. Most engineers are familiar with planar mechanisms such as the planar four-bar shown in Figure 1a. The simplest spatial mechanism, the spherical four-bar, is shown in Figure 1b. The spherical mechanism consists of four links joined by four revolute (4R) joints, all of which have axes of revolution that meet in a single point: the center of the spherical constraint surface transversed by the links. In these closed-chain mechanisms, the motion of each link is affected by the motion of the adjoining links.

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Figure 1. (a) Planar four-bar mechanism (b) Spherical four-bar mechanism

In the late 70s and early 80s, interactive computer graphics design programs were developed for planar mechanism design based on Burmester’s (1886) geometric design procedures. The first computer graphics program was Kaufman’s KINSYN (Kaufman 1978), followed shortly by Erdman’s LINCAGES package (Erdman and Gustafson 1977), and later by Waldron’s RECSYN (Waldron and Song 1981). These programs enable rapid design and analysis of planar linkages, allowing the inventor to survey the dimensions and evaluate the movement of many linkages during one design session.

In the early 1990’s Larochelle and McCarthy turned to interactive workstation-based computer graphics to develop a tool to design spherical mechanisms. For spherical linkages, the first computer-based synthesis techniques were described by Suh and Radcliffe (1967) and Roth (1967). This was later expanded by Dowler et al. (1978). Reinholtz et al. (1986) generalized Filemon’s (1972) ideas for avoiding problematic spherical linkage types. The first interactive graphics-based spherical linkage design system, SPHINX, was developed by Larochelle and McCarthy in 1993 (Larochelle et al. 1993).The user interface to the SPHINX software is shown in Figure 2.

The design of a spherical mechanism using SPHINX is accomplished by first specifying the desired positions and orientations of the coupler link in up to 4 discrete positions. For each design specification, 160,000 mechanisms exist. To limit the solution set to a usable number of alternative solutions, constraints are needed. Two approaches are available to input constraints on the design. The user can either specify the positions of the pivots or choose the type of mechanism that is desired. The first approach is based on selecting the location of the fixed and moving pivots using the congruence cones. The second approach is based on selecting the type of mechanism desired from the 160,000 linkages which are generated by SPHINX from the input design position data. These linkage possibilities are displayed as a color coded map, called the linkage type map, shown in the lower part of Figure 2. Once the constraints are specified, the mechanism is displayed and the designer can animate the movement and edit the final form of the linkage to plan the construction of a prototype.

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Figure 2: SPHINX: Spherical mechanism design

In a related, but independent effort, Scott Osborn, a graduate assistant working with Prof. Vance, developed SphereVR (Figure 3), a virtual reality environment for the design of spherical mechanisms. The approach is slightly different from SPHINX. A 3D mouse is used to place the design positions on the sphere and to press buttons on a virtual menu tablet to specify constraints on the individual link pivot point locations. The linkage type map and the congruence cones are not generated, but rather, the individual link pivot points are constrained to lie on user-specified geometric planes. Once synthesized, the linkage can be animated to examine the motion. The 3D mouse is also used to input commands such as Solve and Animate that appear on the virtual menu tablet. The program can be implemented using a variety of visual display devices including stereo glasses, a head-mounted display or a head-coupled display (BOOM). This allows the designer to move relative to the sphere to view it from a many different viewpoints.

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Figure 3: SphereVR: Spherical mechanism design using VR

Next, Juliet Kraal, another graduate assistant at Iowa State University created VEMECS (Virtual Environment MEChanism Synthesis). This program was displayed in stereo on a projection screen and viewed using CrystalEyes stereo glasses. Interaction with the virtual objects was performed using the Pinch Gloves. A menu system replaced the virtual menu object used in SphereVR. The design process more closely followed the procedure used in the workstation-based SPHINX program.

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Figure 3: VEMECS: Virtual Environment MECHanism Synthesis

Currently, Todd Furlong, a graduate assistant at Iowa State University, is working on the 3rd evolution of the virtual mechanism design application, Isis (Interactive Synthesis of Spherical Mechanisms). The approach now is to provide virtual objects in the environment so that designing the mechanisms can be performed in context. Instead of placing abstract coordinate systems in place on the design sphere, the user places instances of the part that needs to move. Pivots can be selected that relate to the attachment of the mechanism to it’s base part. This program uses CrystalEyes stereo glasses and a projection screen or an n-Vision helmet or the C2 for display. Interaction is provided using the pinch gloves.

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Figure 4: ISIS (Interactive SynthesIS)

Personnel

Professors

The virtual reality environment for spherical mechanism design is a project that is being pursued on three different campuses. At Iowa State University, Professor Judy Vance leads the virtual reality effort. Professor Pierre M. Larochelle at the Florida Institute of Technology and Professor J. Michael McCarthy at the University of California, Irvine are developing new synthesis and analysis theory in the fields of spatial mechanism design that will be incorporated into the virtual environment.

Graduate Students

Undergraduate Students

Images

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1. Planar and Spherical 4 bar Mechanism Definition

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2. Retractable Joystick Using a Spherical Mechanism

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3. Student Desk Spherical Mechanism

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4. AviAuto with wings extended

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5. AviAuto with wings folded

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6. Spherical mechanism design for the AviAuto wings (wings folded)

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7. Spherical mechanism design for the AviAuto wings (wings extended)

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8. Positions placed on the sphere

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9. Completed mechanism

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10. The VR spherical mechanism design steps

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11. Sphinx with guide map

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12. Sphinx showing congruence cones

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13. Sphinx showing final mechanism

VRML

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This links to a VRML representation of the sphere with the linkage, which allows a good look at the linkage in three dimensions.

Quicktime

  • Quicktime movie of user interacting with spherical mechanism program (8.0 MB)

Applications

Two recent projects at the University of California at Irvine (UCI) which were developed using the SPHINX software have resulted in usable spherical four-bar mechanisms: the UCI Hinge and the UCI Joy-stick Support Linkage. The UCI Hinge (Figure 4) was designed to stow the communication table of a wheelchair-bound individual from a position in the lap to a position beside the wheelchair. Traditional means to accomplish this task employ two planar mechanisms attached in series. Here, the spherical mechanism can perform the same motion, providing a smoother transition for the table and using fewer links in the mechanism. The UCI Joy-stick Support Linkage (Figure 5) was designed to deploy the chin joy-stick controller for a quadriplegic from behind a wheelchair into position in front of the operator. This linkage is in use at the Center for Applied Rehabilitation Technology at Rancho Los Amigos Hospital. Used in a manufacturing setting, similar linkages can provide pick and place movements that are equivalent to robotic systems at a much lower cost and complexity.

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Figure 4. UCI Hinge spherical mechanism

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Figure 5. UCI Joy-stick Support Linkage spherical mechanism

A recent project at the Florida Institute of Technology has resulted in the design and manufacture of a spherical four bar mechanism which deploys and retracts the wings on the AviAuto (figure 6) roadable aircraft. The AviAuto is a prototype roadable aircraft, or flying car, that is being developed at Florida Tech. In previous designs of the AviAuto, two planar hinges, each actuated by a stepper motor and gear head, were used to deploy and retract each wing. Implementation of the spherical mechanism design has resulted in significant cost and weight savings.

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Figure 6. AviAuto with wing spread and retracted

Lab Facilities

  • Virtual Reality Applications Center, Iowa State University
  • Florida Tech Robotics & Spatial Systems Laboratory, Florida Institute of Technology
  • UC Irvine Robotics & Automation Laboratory, University of California Irvine

Funding

General information can be found at these NSF web pages:

  • Design and Integration Engineering Program
  • Design, Manufacture, and Industrial Innovation Program
  • Directorate for Engineering