Synthetica 2'0: Software for the Synthesis of Constrained Serial Chains

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Synthetica 2.0 Software for the Synthesis of
Constrained Serial Chains
ASME 28th Biennial Mechanisms and Robotics
Conference Salt Lake City, Utah, September 28 to
October 2, 2004 2004 INTERNATIONAL DESIGN
ENGINEERING TECHNICAL CONFERENCES and COMPUTERS
INFORMATION IN ENGINEERING CONFERENCE

• Alba Perez,
• College of Engineering, Idaho State University
• Hai Jun Su, J. Michael McCarthy,
• Robotics and Automation Laboratory, University
  of California, Irvine

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Linkage Design Software

• Commercial computer-aided design packages
• Drawing
• CAM integration
• Motion analysis / inverse kinematics
• Force analysis / dynamic simulation
• Stress/strain analysis / FEA
• Commercially available function-to-form software
• SyMech
• planar 4 to 12-bar linkages.
• WATT (Heron technologies)
• planar 4, 6, and 8-bar linkages.
• SAM (Artas)
• planar 4-bar linkage, other for specific
  applications.

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Background
Research software

• Planar linkage design
• LINCAGES, Erdman and Gustafson, 1977.
• RECSYN, Waldron and Song, 1981.
• Spherical linkage design
• SPHINX, Ruth and McCarthy, 1997.
• Spatial linkage design
• SPADES, Kihonge, Vance and Larochelle, 2002.
• Synthetica 1.0, Su, Collins and McCarthy, 2002.

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Synthetica 1.0 presented at the ASME DETC 2002
conference
Animation Bar
Data I/O
Object Tree
GL4Java Viewer
Info Panel
Teach Panel
Work piece
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Synthetica 1.0

• Features
• Loading synthesis and analysis routine.
• Synthesize/create linkages
• Edit, import and export linkage data.
• Analyze (forward and inverse kinematics).
• Display/Animate.

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Synthetica 2.0

• The synthetica 2.0 version presents the following
  added capabilities
• Generic synthesizer
• Specialized synthesis routines
• Selection matrix
• Improved interpolation and animation capabilities

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Generic Synthesizer
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Generic Synthesizer

• Default design procedure to be used when there is
  no specialized design routine.
• A total of 120 topologies consisting of R, P, C,
  T and S joints and ranging from 2 to 5 degrees of
  freedom.
• Design equations are created by equating the dual
  quaternion synthesis equations to the task
  positions.
• A counting formula allows to assign serial chain
  topologies to each task.
• Java translation of FORTRAN Minpack numerical
  solver (Steve Verrill, translator).

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Generic Synthesizer
To formulate the design equations, write the
kinematics equations using the Clifford algebra
of dual quaternions,
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Generic Synthesizer
Equate the kinematics equations to the set of
task positions,
to solve numerically for the coordinates of the
joint axes, Si, and the values of the joint
variables to reach each task position.
Counting equations and unknowns for each
topology, there exists a maximum number of task
positions that can be specified
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Generic Synthesizer

• Some examples
• RR, 3 positions 83msec
• RRR, 5 positions 1.55sec
• TC, 6 positions 245 msec
• TRP, 7 positions 4.73sec
• RCC, 7 positions 2.26sec
• RPRR, 8 positions 2.69sec
• SC, 8 postions 6.76sec
• RTR, 8 positions 5.20sec
• RRRR, 9 positions 6.35sec.
• SPR, 10 positions 49.72sec.

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Specialized Synthesis Routines
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Specialized Synthesis Routines

• Eight routines that solve specific topologies.
• Faster than numerical solver.
• Based on algebraic solutions, return all
  solutions for a given chain.
• New synthesis routines developed by external
  users can be integrated into the program.

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Specialized Synthesis Routines

• Robots with spherical wrists (Su 2004)
• Designed for reachable surfaces and solved using
  resultant elimination.
• Implemented chains CS-3, CS-6, RPS-8, TS-3.

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Specialized Synthesis Routines

• Dual quaternion design equations (Perez 2003)
• For some chains, it is possible to find
  algebraic solutions by eliminating the joint
  variables.
• Implemented chains RP-2, PR-2, RR-3, RPC-5.

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Other Features
Bezier interpolation with double quaternions
Selection matrix
Trajectory approximation
Motion simulation
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Conclusions

• Synthetica is a Java-based software for the
  synthesis, visualization, analysis and simulation
  of spatial linkages.
• The new release, Synthetica 2.0, was presented.
• Synthetica 2.0 incorporates a general numerical
  synthesizer for the design of 120 serial chains.
• It also incorporates 8 specialized synthesis
  routines that return all the solutions for a
  given task and topology.
• Future directions include
• Optimization of the numerical solver for
  increased speed.
• Generation of new specialized synthesis routines.
• Integration with commercially available CAD
  software.
• Synthetica 2.0 for PC or Mac can be downloaded
  from http//synthetica.eng.uci.edu