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

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

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.

Synthetica 1.0: presented at the ASME DETC 2002 conference

Data I/O Object Tree Animation Bar GL4Java Viewer Info Panel Teach Panel Work piece

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, d 5 S 5  5 S 3  3 d 3 d 2 S 2  2 S 1  1 d 1  4 d 4 S 4

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

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.

15 26 186 216 588 804 Roots 1 3 4 4 7 8 11 Time <<1s <<1s <<1s <<1s <<1s <<1s <<1s <<1s 0.04s

6m 16m 14m 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