Virtual Prototyping of Mechanical Assemblies in
Alpha_1's Design Variation Studio


Concurrent manipulation and design optimization are possible in augmented coordinates [dnelson99][dnelson98] at kilohertz rates. This ability to visualize kinematic reach and collision workspace during the optimization of a mechanical design objective is the next step in mouse and haptics interaction with CAD models. See also advanced work on solid finger tracing and assembly surface constraints Fast Surface Gradients for Solving Time-Varying Contact Constraints, Haptics Tracing, and Collision Dynamics (write dnelson@cs.utah.edu for the password). By using augmented coordinates, we establish joint constraints at a local scope; that is, joints are defined as constraints rather than with joint angles or other reduced coordinates. Problems with kinematic loops, such as in Stewart platforms, 4 bar mechanisms, largely go away. Also, the ability to write surface contact and nonholonomic constraints is also possible in augmented coordinates. The analysis of a mechanism's closed loop inverse dynamics can be done in linear time using this formulation[dnelson99], a superior approach to an earlier method [nahvi,dnelson98].
  • Multielement Flexible Body Manipulation
  • Single Flexible Body Manipulation
  • 4 Bar, 1 DOF Spatial Mechanism
  • Prismatic Stewart Platform
  • Universal, Spherical, and Revolute Joint Stewart Platform
  • 4 Bar Mechanism Driving a Universal Joint
  • Peaucellier Mechanism
  • Stewart Platform Manipulation/Optimization
  • Spatial 4 Bar Manipulation/Optimization
  • Spatial Cam Self-Assembly and Manipulation, wireframe inside look
  • Thin Flexible Elements
  • Finger Surface Tracing

    The haptic interaction with assemblies also requires tracing mechanical surfaces with point contact [tthompso,dnelson97], or in a more recent development, with a parametric surface model for the finger. Previous efforts with point-to-surface tracing have used offset surfaces to give a finger a spherical volume. Surface tracing with a solid finger model is a more natural, intuitive approach that the previous work in point tracing. Both methods are local algorithms in that global minimal distance computations are required. The local property allows them to run at an update rate in excess of 10kHz.
  • Thumb Surface Tracing the Goblet, Velocity Formulation
  • Finger Model Tracing a Bust,another view
  • Finger Volume Rotating
  • Dolphin Model Trace
  • Well-defined Finger Penetration, using the velocity method. Newton-Iterative problems during penetration. Newton-Iteration with cross products has worse problems.
  • Reformulated Newton method solves the penetration irregularities.
  • Virtual proxies are important in the penetrating case. The maximal distance is required by the haptics tracing algorithm. Global discontinuities such as "chopping though" an object are not desirable. Because a haptics device such as a PHANToM can hold a user to within .3mm of the surface, local discontinuities should not occur except for regions of very high curvature. Since the velocity formulation is the "most local", it is the distance computation of choice for tracing surface updates for the penetrating case.

    Optimization and Graph Theory

    The manipulation performance of large models is also a concern in this work. We use a linear time (given certain mild assumptions) optimization algorithm to perform the "self-assembly" or interactive reassembly/inverse kinematics tasks required for concurrent optimization and manipulation. Our optimization method is organized around graph-theoretic results from the mechanical engineering community.
  • Spherical Joint Dynanics
  • Planar Slider Crank, 1 DOF
  • Spatial 4 Bar Mechanism, 1 DOF
  • Closed Loop, Revolute Joints
  • Participants


    o Nelson, D. D., Johnson, D., and Cohen, E., "Haptic Rendering of Surface-to-Surface Sculpted Model Interaction," in Proc. 8th Annual Symp. on Haptic Interfaces for Virtual Environment and Teleoperator Systems, (Nashville, TN), ASME, November 1999.
    [PDF] [PS]
    o Nelson, D. and Cohen, E., "Interactive Mechanical Design Variation for Haptics and CAD," September 1999. Accepted at EUROGRAPHICS 99.
    o Thompson II, T. V., Nelson, D. D., Cohen, E. C., and Hollerbach, J. M., "Manueverable Models Within A Haptic Virtual Environment," in Proc. 6th Annual Symp. on Haptic Interfaces for Virtual Environment and Teleoperator Systems, (Dallas, TX), pp. 37-44, ASME, November 1997.
    o Hollerbach, J., Cohen, E., Thompson, W., Freier, R., Johnson, D., Nahvi, A., Nelson, D., Thompson II, T., and Jacobsen, S., "Haptic Interfacing for Virtual Prototyping of Mechanical CAD Designs," in Proc. Design for Manufacturing Symposium, (Sacramento, CA), ASME, September 1997.
    [dnelson00] IEEE VR2000 Optimization-Based Virtual Surface Contact Manipulation at Force Control Rates

    [nahvi,dnelson98] 1998 IEEE International Conf. Robotics & Automation,Haptic Manipulation of Virtual Mechanisms From Mechanical CAD Designs

    [group97] 1997 ASME Haptic Interfacing For Virtual Prototyping Of Mechanical CAD Designs


    Support for this research was provided by NSF Grant MIP-9420352, by DARPA grant F33615-96-C-5621, and by the NSF and DARPA Science and Technology Center for Computer Graphics and Scientific Visualization (ASC-89-20219).

    Last update: January 7, 2000