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