Method and apparatus for design and optimization for simulation of motion of mechanical linkages

• US 5,297,057 A
• Filed: 11/13/1991
• Issued: 03/22/1994
• Est. Priority Date: 06/13/1989
• Status: Expired due to Fees

• Current Assignee: Schlumberger Technologies Incorporated (Schlumberger NV)
• Original Assignee: Schlumberger Technologies Incorporated (Schlumberger NV)
• Inventors: Bodner, Michael E., Cooper, Jeffrey G., Turner, Patrick R., Barrow, Harry G., Kramer, Glenn A.
• Primary Examiner(s): Black, Thomas G.
• Assistant Examiner(s): ZANELLI, MICHAEL J
• Application Number:
  US07/793,303
• Time in Patent Office: 860 Days
• Field of Search: 364/512, 364/578, 364/505, 340/725, 358/104, 395/152
• US Class Current: 703/7
• CPC Class Codes: G06F 30/17 Mechanical parametric or variational design
• CPC Class Codes: Y10S 345/953 Geometric processing

Abstract

A method and apparatus for performing kinematic analysis of linkages using generalized mechanisms selected from a catalog of mechanisms. From an initial selection of mechanisms, the one most closely matching a desired behavior is chosen and an optimization procedure is conducted. The method may be preceded by a qualitative kinematic analysis or the qualitative analysis may be used in lieu of a catalog selection. An improved optimization technique and a closed form kinematic analysis method is described.

Claims

1. A method of performing synthesis of mechanical linkages in a digital computer comprising the steps of:

a) optimizing a design so as to minimize at least one deviation from desired behavior; and

b) displaying on a video display a simulated motion of said design and a relative contribution of at least two parameters to deviations from desired behavior to a total deviation from desired behavior, said total deviation comprised of a sum of individual deviations from desired behavior, said individual deviations are weighted.

2. A method of performing synthesis of mechanical linkages in a digital computer comprising the steps of:

a) providing a plurality of symbolic constraints for interface with said user, said symbolic constraints translated to penalty functions in said digital computer;

b) optimizing a design so as to minimize at least one deviation from desired behavior, said design includes any one of said plurality of symbolic constraints; and

c) displaying on a video display a simulated motion of said design and a relative contribution of at least two parameters to deviations from desired behavior to a total deviation from desired behavior, said total deviation comprised of a sum of individual deviations from desired behavior.

13. The computer as recited in claim 2, wherein said first and said second errors are represented by a sum of squares of error.

3. A method for performing a simulation of motion of a mechanical linkage, said simulation selecting a plurality of design parameters, said simulation performed in a digital computer having a video animation display for animating said linkage, comprising the steps of:

a) inputting a first set of said plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) determining a near optimum step direction vector for adjusting each of said design parameters to provide a behavior of said linkage closer to said desired behavior, said near optimum step direction vector decreasing an error function from one set of said design parameters to a next set of said design parameters, said step of determining a near optimum step direction using at least one interdependency between said design parameters and said error function;

c) based on said near optimum step direction, substantially reducing a value of said error function; and

d) animating the motion of said linkage with said next set of design parameters on said video animation display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.

4. The method as recited in claim 3, wherein said step direction vector is defined by an equation of the form:

##EQU12## where;

γ

is;

a+λ

if j=k;

a if j≠

k;

d_i are error terms;

p_k is a k^th parameter of a parameter vector;

p_j is a j^th parameter of a parameter vector;

δ

is a step in parameters being solved;

i is a counter for error terms;

j is a counter for matrix row;

k is a counter for matrix column;

λ

is a variable which controls variation between steepest and linear-interdependent modes of calculating step direction; and

a is a constant greater than 0 and less than or equal to 1.

5. A method of performing simulated motion of a mechanical linkage with near optimum parameters for said mechanical linkage, said optimum parameters producing desired linkage behavior within error limits, comprising the steps of:

a) inputting a first set of a plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) calculating a first error between behavior of said linkage with said first set of design parameters and said desired behavior;

c) calculating a step size vector for said parameter vector, said step size vector adjusted for interdependencies among said design parameters influence on said first error;

d) evaluating a second error using said step size vector;

e) moving between steepest-descent and linear-interdependent modes of calculating step direction based on a direction of change between said first and said second errors to calculate said near optimum parameters; and

f) animating said simulated motion of said linkage with said near optimum parameters on a video animation display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.

6. The method as recited in claim 5, wherein said step of calculating a step size vector uses a Jacobian matrix composed of gradients of constraints with respect to each parameter.

7. The method as recited in claim 5, wherein said optimization uses a kinematic solver to calculate behavior of said linkage.

8. The method as recited in claim 5, wherein said optimization uses a closed form system to calculate behavior of said linkage.

9. The method as recited in claim 5, wherein said first and said second errors are represented by a sum of squares of error.

10. A digital computer for performing simulation of motion of a mechanical linkage on a video animation display and programmed to:

a) input a first set of a plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) determine a near optimum step direction vector for adjusting each of said design parameters to provide a behavior of said linkage closer to said desired behavior, said near optimum step direction vector decreasing an error function from one set of said design parameters to a next set of said design parameters, said step of determining a near optimum step direction using at least one interdependency between said parameters and said error function;

c) based on said near optimum step direction, substantially reduce a value of said error function to produce a linkage design which traces a path closer to a desired path; and

d) animate motion of said linkage with said next set of design parameters on said video animation display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.

11. The computer as recited in claim 10, wherein said direction vector is defined by an equation of the form:

##EQU13## where;

γ

is;

a+λ

if j=k;

a if j≠

k;

d_i are error terms;

p_k is a k^th parameter of a parameter vector;

p_j is a j^th parameter of a parameter vector;

δ

is a step in parameters being solved;

i is a counter for error terms;

j is a counter for matrix row;

k is a counter for matrix column;

λ

is a variable which controls variation between steepest and linear-interdependent modes of calculating step direction; and

a is a constant greater than 0 and less than or equal to 1.

12. A digital computer for performing simulated motion of a mechanical linkage with near optimum parameters for said mechanical linkage, said optimum parameters producing desired linkage behavior within error limits, said digital computer programmed to:

a) input a first set of a plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) calculate a first error between behavior of said linkage with said first set of design parameters and said desired behavior;

c) calculate a step size vector for a vector of said set of design parameters, said step size vector adjusted for interdependencies among said design parameters influence on said first error;

d) evaluate a second error using said step size vector;

e) move between steepest-descent and linear-interdependent modes of calculating step direction based on a direction of change a between said first and said second errors to calculate said near optimum parameters; and

f) animate said simulated motion of said linkage with said near optimum parameters on a video animation of display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.

14. The computer as recited in claim 12, wherein said computer is programmed to calculate a step size vector using a Jacobian matrix composed of gradients of constraints with respect to each design parameter.

15. The computer as recited in claim 12, wherein said computer is programmed to optimize using a kinematic solver to calculate behavior of said linkage.

16. The computer as recited in claim 12, wherein said computer is programmed to optimize using a closed form system to calculate behavior of said linkage.

17. A method for performing a simulation of motion of a mechanical linkage, said simulation selecting a plurality of design parameters, said simulation performed in a digital computer having a video animation display for animating said linkage, comprising the steps of:

a) inputting a first set of said plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) determining a near optimum step direction vector for adjusting each of said design parameters to provide a behavior of said linkage closer to said desired behavior, said near optimum step direction vector decreasing an error function from one set of said design parameters to a next set of said design parameters, said step of determining a near optimum step direction using at least one interdependency between said design parameters and said error function, said near optimum step direction vector is defined by an equation of the form;

##EQU14## where;

γ

is;

a+λ

if j=k;

a if j≠

k;

d_i are error terms;

p_k is a k^th parameter of a parameter vector;

p_j is a j^th parameter of a parameter vector;

δ

is a step in parameters being solved;

i is a counter for error terms;

j is a counter for matrix row;

k is a counter for matrix column;

λ

is a variable which controls variation between steepest and linear-interdependent modes of calculating step direction and a is a constant greater than 0 and less than or equal to 1;

c) based on said near optimum step direction, substantially reducing a value of said error function; and

d) animating the motion of said linkage with said next set of design parameters on said video animation display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.

18. A digital computer for performing simulation of motion of a mechanical linkage on a video animation display and programmed to:

a) input a first set of a plurality of design parameters for said mechanical linkage, and a desired behavior of said linkage, said plurality of design parameters indicative of link lengths and joint positions in said mechanical linkage, said desired behavior indicative of a path to be traced by at least a portion of said mechanical linkage;

b) determine a near optimum step direction vector for adjusting each of said design parameters to provide a behavior of said linkage closer to said desired behavior, said near optimum step direction vector decreasing an error function from one set of said design parameters to a next set of said design parameters, said step of determining a near optimum step direction using at least one interdependency between said design parameters and said error function, said near optimum direction vector is defined by an equation of the form;

##EQU15## where;

γ

is;

a+λ

if j=k;

a if j≠

k;

d_i are error terms;

p_k is a k^th parameter of a parameter vector;

p_j is a j^th parameter of a parameter vector;

δ

is a step in parameters being solved;

i is a counter for error terms;

j is a counter for matrix row;

k is a counter for matrix column;

λ

is a variable which controls variation between steepest and linear-interdependent modes of calculating step direction, and a is a constant greater than 0 and less than or equal to;

c) based on said near optimum step direction, substantially reduce a value of said error function to produce a linkage design which traces a path closer to a desired path; and

d) animate motion of said linkage with said next set of design parameters on said video animation display, said animation tracing a path of said at least a portion of said mechanical linkage during motion of said mechanical linkage.