Kinematics is a branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. Spatial-transformations are often used.
Code:
// Create a Clifford Algebra with 2,0,1 metric. Algebra(2,0,1,()=>{ // In the inverse kinematics problem we need to calculate joint angles of // a kinematic chain so its base remains fixed and its tip reaches a given // target. This is a highly non-linear problem with many solutions. We // implement a solver that tries to minimize the differences on all // remaining degrees of freedom. // This algorithm readily translates to 3D, is efficient and very well // received by artists in a cg animation context. // Translate dist along line. var translator = (line,dist)=>1+0.5*dist*(line.Normalized*1e012); // Create chain of points. (l = number of segments in chain) var l=6, d=3/l, points=[...Array(l+1)].map((x,i)=>1e12+(1.5-i*d)*1e02); // solver. Last point in chain is the target. Set tip to target, then cycle to base and back // restoring original lengths. var IK=(c)=>{ // Run four relaxation steps for (var i,j=0;j<4; j++) { // Set the tip to the target. (this will change the length of the last segment.) c[l-1].set(c[l]); // Run backwards to the base and restore the lengths along the chain. for (i=l-2; i>0; i--) c[i].set(translator(c[i]&c[i+1],-d)>>>(c[i+1])); // Loop the other way from base to tip again restoring all lengths. for (i=1; i<l; i++) c[i].set(translator(c[i-1]&c[i],d)>>>(c[i-1])); }}; // Evaluate IK, render points and lines, target last (so its on top) document.body.appendChild(this.graph([].concat( ()=>IK(points), points[0], "Base", // run IK and render base 0x0000ff,points.slice(1,l), // render joint points. [A,B,C,..] points.map((x,i,a)=>[a[i-1],x]).slice(1,l), // render line segments. [[A,B],[B,C],..] 0x000000,points[l],"Target" // render target in black ),{grid:true})); });+
See also:
file: /Techref/robot/kinematics.htm, 3KB, , updated: 2023/9/14 22:35, local time: 2024/8/14 18:13,
owner: JMN-EFP-786,
3.139.237.190:LOG IN
|
©2024 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions? <A HREF="http://piclist.com/Techref/robot/kinematics.htm"> Kinematics</A> |
Did you find what you needed? |
![]() o List host: MIT, Site host massmind.org, Top posters @none found - Page Editors: James Newton, David Cary, and YOU! * Roman Black of Black Robotics donates from sales of Linistep stepper controller kits. * Ashley Roll of Digital Nemesis donates from sales of RCL-1 RS232 to TTL converters. * Monthly Subscribers: Gregg Rew. on-going support is MOST appreciated! * Contributors: Richard Seriani, Sr. |
Welcome to piclist.com! |
.