vision system++convert position value to motor angle

hi do any boday have a idea about this video

http://www.youtube.com/watch?v=ZuvsUZGdJOo

how they convert position of object to angle ???

 whichs method available??

Answer 1

[Roger Stafford]

The robot "arm" can be considered as composed of four segments connecting five points. Point A is at the base of the central pivot on the horizontal plane, point B is directly above A at the first joint, point C is the second joint, point D is the third joint, and point E hangs directly below D and above the plane ready to pick up the object. Let the length of segment AB be called a, the length of BC be b, the length of CD be c, the length of DE be d and let point E be a distance e above the horizontal plane. As you recall I called the horizontal plane coordinates of the point A (0,0) and the those of the object on the plane to be picked up (x,y). We want to use all these these data to determine the three angles ABC, BCD, CDE which must be achieved by the motors at the three joints, B, C, and D.

The computation goes as follows.

 r = sqrt(x^2+y^2); % Horizontal distance from object to base
 s = sqrt(r2+(a-d-e)^2); % Distance between B and D
 angleBDE = pi/2+atan2(a-d-e,r);
 angleABD = pi - angleBDE;
 angleCBD = acos((b^2+s^2-c^2)/(2*b*s)); % Cosine law of triangles
 angleCDB = acos((c^2+s^2-b^2(/(2*c*s)); %    "    "  "      "
 angleABC = angleABD+angleCBD;
 angleCDE = angleCDB+angleBDE;
 angleBCD = pi-angleCBD-angleCDB;

These last are the three required angles, all in radians. I already computed the azimuth angle of the motor at the base for you.

Answer 2

[Roger Stafford]

I see four different angles involved in the positioning of the robot arm in that video. Which one or ones are you inquiring about?

I'll show you how the azimuth angle is calculated. If x and y are cartesian coordinate in the plane of the horizontal surface there and the origin is located at the central (vertical) axis of the arm's base, then the angle in radians with respect to whatever is the x-axis (going counterclockwise) is:

 a = atan2(y,x);

The other three angles in the vertical plane are similarly simple angles to calculate using elementary trigonometry. Do you want to know about these also?

[mangood UK]

dear for the problem above in YouTube

can we find the angle of arm using geometric approach???

what about the orientation???

best regards