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Synthetica 2.0: Software for the Synthesis of Constrained Serial Chains
Alba Perez, College of Engineering, Idaho State University
Hai Jun Su, J. Michael McCarthy, Robotics and Automation Laboratory, University of
California, Irvine
ASME 28th Biennial Mechanisms and Robotics ConferenceSalt Lake City, Utah, September 28 to October 2, 2004
2004 INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES
and COMPUTERS & INFORMATION IN ENGINEERING CONFERENCE
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.
Background
• 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.
Research software:
Synthetica 1.0: presented at the ASME DETC 2002
conference
Object Tree
Info Panel
Teach Panel
Work piece
GL4Java Viewer
Animation Bar
Data I/O
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.
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
Generic Synthesizer
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).
Generic Synthesizer
To formulate the design equations, write the kinematics equations using the Clifford algebra of dual quaternions,
S1S2S3
S4
S5θ1θ2
θ3
θ4
θ5d1
d2d3
d4
d5
Generic Synthesizer
Counting equations and unknowns: for each topology, there exists a maximum number of task positions that can be specified
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.
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.
Specialized Synthesis Routines
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.
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.
Roots Time
1 <<1s
3 <<1s
4 <<1s
4 <<1s
7 <<1s
8 <<1s
11 <<1s
15 <<1s
26 0.04s
186 6m
216 16m
588 14m
804 1h02m
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.
Other Features
Selection matrix Bezier interpolation with double quaternions
Trajectory approximation Motion simulation
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