歯車について勉強する3 の履歴(No.3)

歯車を描く†

LANG: p5js_live
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0===this.option?.stroke?t.stroke("black"):t.stroke(this.option.stroke),void 0===this.option?.weight?t.strokeWeight(1):t.strokeWeight(this.option.weight),void 0===this.option?.dash?t.drawingContext.setLineDash([]):t.drawingContext.setLineDash(this.option.dash),void 0===this.option?.fill){t.noFill(),t.beginShape();for(let e=0;e<this.length;e++)t.vertex(this[e].x,this[e].y);t.endShape()}else{t.fill(this.option.fill),t.beginShape();for(let e=0;e<this.length;e++)t.vertex(this[e].x,this[e].y);t.endShape(t.CLOSE)}e&&this.forEach(e=>t.circle(e.x,e.y,1.5))}apply(t,e=this.option){return new l(e,...this.map(t))}crossPoint(t){return s(this[0],this[1],t[0],t[1])}direction(t=0){return this[t].sub(this[t+1]).normalize()}}function s(t,e,n,i){let r=e.sub(t),l=i.sub(n),s=n.sub(t),a=r.outer(l);if(0==a)return;let h=s.outer(r)/a,o=s.outer(l)/a;if(!(h<0)&&!(h>1)&&!(o<0)&&!(o>1))return t.add(r.mul(o))}function a(t,e,n){let i=n.sub(e),r=t.sub(e);return Math.abs(i.outer(r)/i.norm())}function 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t=0;t<=60;t+=S){let r=u+(c-u)*t/60,l=n(r);P||l.norm()>o.norm()&&l.sub(o).angle()<x||(P=!0,C=r,I&&(E.push(I),N.push(r-(c-u)*S/60))),P&&(E.push(l),N.push(r));let h=e(r,s);if(t>0&&h.sub(e(w,s)).norm()<b/1e3){let t=f(l.sub(e(w,s)).angle()),n=m-m/v/2+k,r=d(f(n-t)/m*180);for(let l=1;l<=r;l++){let h=t+(n-t)*l/r;E.push(e(w,s).add(i.polar(a,h)))}break}t>0&&l.sub(I).norm()>b/20&&(S/=2),I=l}return u=C,[E,N]}(t,g,v,m,d,f),{cInvolute:y,involuteT:k,cFillet:M,filletT:z}=function(t,e,n,i,r,l){let[o,u,c]=function(t,e){let n=0,i=0;for(;n<t.length-1&&i<e.length-1;){if(t[n+1].x>e[i].x){n++;continue}if(t[n].x<e[i+1].x){i++;continue}let r=s(t[n],t[n+1],e[i],e[i+1]);if(r)return[r,n,i];t[n+1].x>e[i+1].x?n++:i++}return[]}(t,i);if(o)t.splice(u+1,1/0,o),e.splice(u+1,1/0,h(e[u],e[u+1],t=>n(t)[0].sub(o).norm())),i.splice(0,c+1,o),r.splice(0,c+1,h(r[c],r[c+1],t=>l(t).sub(o).norm()));else{let[s,o,u,c]=function(t,e){let 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r=n(i,"ツールを非表示",27.5,0),l={m:e(i,"ﾓｼﾞｭｰﾙ",0,{min:10,max:200,value:40,step:1}),alpha:e(i,"圧力角",1,{min:10,max:32,value:20,step:1}),z:e(i,"歯数A",2,{min:4,max:200,value:19,step:1}),shift:e(i,"転位A",3,{min:-.5,max:2,value:0,step:.05}),z2:e(i,"歯数B",4,{min:4,max:200,value:6,step:1}),shift2:e(i,"転位B",5,{min:-.5,max:2,value:0,step:.05}),fillet:e(i,"ﾌｨﾚｯﾄ",6,{min:0,max:.4,value:.4,step:.01}),backlash:e(i,"ﾊﾞｯ

ｸﾗｯｼｭ",7,{min:0,max:2,value:0,step:.01}),velocity:e(i,"速度",8,{min:-1,max:10,value:1,step:.1}),theta:e(i,"回転角",9,{min:-180,max:180,value:0,step:.05}),df:n(i,"歯底円",10.5,0,!1),db:n(i,"基礎円",10.5,1,!1),dp:n(i,"基準円",10.5,2,!0),dk:n(i,"歯先円",10.5,3,!1),play:n(i,"自動更新",11.5,0,!0),connection:n(i,"接続点",11.5,1,!1),inner:n(i,"内歯車",11.5,2,!1),stop:!1};return t.forEach*1e,n)=>{e.style("opacity","0.2"),e.mouseOver*2)=>t.forEach(t=>t.style("opacity","1"(#notefoot_2)),e.mouseOut*3)=>t.forEach(t=>t.style("opacity","0.2"(#notefoot_3))}),l.theta.mousePressed*4)=>{l.stop=!0}),l.theta.mouseReleased*5)=>{l.stop=!1}),r.elt.onchange=()=>{t.forEach*6t,e)=>{e<2||(r.checked()?t.hide():t.show((#notefoot_6)})},{get m(){return Number(l.m.value((#notefoot_5)},get alpha(){return Number(l.alpha.value((#notefoot_4)/180*Math.PI},get z(){return Number(l.z.value(},get shift(){return Number(l.shift.value())*this.m},get z2(){return Number(l.z2.value())},get shift2(){return Number(l.shift2.value())*this.m},get theta(){return-(Number(l.theta.value())/180)*Math.PI},set theta(value){l.theta.value(-(180*value)/Math.PI),l.theta.elt.oninput()},get fillet(){return Number(l.fillet.value())*this.m},get mk(){return+this.m},get mf(){return 1.25*this.m},get backlash(){return Number(l.backlash.value())/100*2*Math.PI/this.z},get play(){return l.play.checked()&&!l.stop},get velocity(){return Number(l.velocity.value())/180*Math.PI},get df(){return l.df.checked()},get db(){return l.db.checked()},get dp(){return l.dp.checked()},get dk(){return l.dk.checked()},get connection(){return l.connection.checked()},get inner(){return l.inner.checked()}}}(i)},i.draw=()=>{var t,e,n;let h;let{ox:u,oy:d}=l;i.background(220);let{gear1:g,gear2:x}=(t=r,h=null!==c?Object.keys(e=c).filter(n=>t[n]!==e[n]):[],(!f||h.filter(t=>!["m2","shift2"].includes(t)).length>0)&&(f=o(t)),(!m||h.filter(t=>!["m","shift","inner"].includes(t)).length>0)&&(m=o({...t,z:t.z2,shift:t.shift2,inner:!1})),n=t,c=["m","z","alpha","shift","z2","shift2","fillet","backlash","inner"].reduce*7t,e)=>(t[e]=n[e],t),{}),{gear1:f,gear2:m});r.play&&(r.theta-r.velocity<-Math.PI?r.theta+=-r.velocity+2*Math.PI:r.theta+=-r.velocity),s(i,g,r.inner?u+r.m*r.z/2-r.shift:u-r.m*r.z/2-r.shift,d,r.inner?r.theta/r.z+Math.PI+Math.PI/r.z:-r.theta/r.z,r.connection,r.inner?r.m*(5+r.z)/2+r.shift:0),s(i,x,u+r.m*r.z2/2+r.shift2,d,r.theta/r.z2+Math.PI+Math.PI/r.z2,r.connection),a(i,r.inner?u+r.m*r.z/2-r.shift:u-r.m*r.z/2-r.shift,d,r),a(i,u+r.m*r.z2/2+r.shift2,d,{...r,z:r.z2,shift:r.shift2})};let s=(t,e,n,i,r=0,l=!1,s=0)=>{t.strokeWeight(1),t.stroke("black"),t.fill("white"),s&&(t.circle(n,i,2*s),t.fill(220,t.beginShape(),e.curve.forEach(e=>{t.vertex(n+e[0]*Math.cos(e[1]+r),i+e[0]*Math.sin(e[1]+r))}),t.endShape("close"),l&&e.connections.forEach(e=>{t.circle(n+e[0]*Math.cos(e[1]+r),i+e[0]*Math.sin(e[1]+r),2)})},a=(t,e,n,i)=>{let{df:r,db:l,dp:s,dk:a,m:h,z:o,mk:u,mf:c,alpha:f,shift:m}=i;t.strokeWeight(1),t.stroke("Blue"),t.noFill(),t.drawingContext.setLineDash([2,6]),r&&t.circle(e,n,(h*o/2-c+m)*2),l&&t.circle(e,n,h*o*Math.cos(f)),s&&t.circle(e,n,h*o),a&&t.circle(e,n,(h*o/2+u+m)*2),t.drawingContext.setLineDash([])}})(p);

内歯車について：

• インボリュート曲線部分のみで歯形としている
• フィレットは付けていない
• 内歯車の転位には対応していない
  • どうやら逆向きに動かしてしまっている？？？ ← TODO

はすば歯車設計†

LANG:p5js_live
function input(i, label, value, func) {
  p.createSpan(label).position(0, 26 * i + 10);
  myInput = p.createInput(value).position(150, 26 * i + 10);
  if (func) {
    myInput.input(func);
  } else {
    myInput.elt.disabled = true;
  }
  return myInput;
}

const inputs = {};

const recalc = () => {
  inputs.pitch.value(inputs.m.value() * Math.PI);
  inputs.mn.value(
    inputs.m.value() / Math.cos((inputs.beta.value() / 180) * Math.PI)
  );
  inputs.pitchn.value(inputs.mn.value() * Math.PI);
  inputs.dp.value(inputs.mn.value() * inputs.z.value());
}

p.setup = () => {
  p.createCanvas(300,240)
  inputs.m = input(1, "歯直角モジュール", 4, recalc);
  inputs.z = input(2, "歯数", 12, recalc);
  inputs.beta = input(3, "ねじれ角", 0, recalc);
  inputs.pitch = input(5, "歯直角ピッチ", 0);
  inputs.mn = input(6, "正面モジュール", 4);
  inputs.pitchn = input(7, "正面ピッチ", 0);
  inputs.dp = input(8, "基準円直径", 0);

  recalc();
}

ウォームギア設計†

LANG:p5js_live
function input(i, label, value, func) {
  p.createSpan(label).position(0, 20 * i + 10);
  myInput = p.createInput(value).position(150, 20 * i + 10);
  if (func) {
    myInput.input(func);
  } else {
    myInput.elt.disabled = true;
  }
  return myInput;
}

const inputs = {};

function recalc() {
  inputs.beta.value(Math.asin(inputs.n.value() * inputs.m.value() / inputs.dp.value())/Math.PI*180)
  inputs.pitch.value(inputs.m.value() * Math.PI);
  inputs.mn.value(
    inputs.m.value() / Math.cos((inputs.beta.value() / 180) * Math.PI)
  );
  inputs.pitchn.value(
    Math.PI * inputs.mn.value()
  );
  inputs.vdp.value(
    inputs.dp.value()/Math.sin(inputs.beta.value()/180*Math.PI)
  )
}

p.setup = () => {
  p.createCanvas(300,240)
  inputs.m = input(1, "歯直角モジュール", 4, recalc);
  inputs.dp = input(2, "基準円直径", 30, recalc);
  inputs.n = input(3, "条数", 1, recalc);
  inputs.pitch = input(5, "歯直角ピッチ", 0);
  inputs.beta = input(6, "ねじれ角", 0);
  inputs.mn = input(7, "正面モジュール", 4);
  inputs.pitchn = input(8, "正面ピッチ", 0);
  inputs.vdp = input(9, "仮想基準円直径", 0)

  recalc();
}