平面機構模擬 Brython 參考程式

fourbar.py

# http://mde.tw/2017springcd/blog/brython-2d-canvas-fourbar.html
# http://project.mde.tw/blog/pyslvs_triangle_expression.html
# http://lab.kmol.info/2017fall/blog/kmol-2017-fall-cadp-fourbar-three-position-synthesis.html
from browser import document
import math
import time
from browser import timer

class Coord(object):
    def __init__(self,x,y):
        self.x = x
        self.y = y

    def __sub__(self,other):
        # This allows you to substract vectors
        return Coord(self.x-other.x,self.y-other.y)

    def __repr__(self):
        # Used to get human readable coordinates when printing
        return "Coord(%f,%f)"%(self.x,self.y)

    def length(self):
        # Returns the length of the vector
        return math.sqrt(self.x**2 + self.y**2)

    def angle(self):
        # Returns the vector's angle
        return math.atan2(self.y,self.x)

def normalize(coord):
    return Coord(
        coord.x/coord.length(),
        coord.y/coord.length()
        )

def perpendicular(coord):
    # Shifts the angle by pi/2 and calculate the coordinates
    # using the original vector length
    return Coord(
        coord.length()*math.cos(coord.angle()+math.pi/2),
        coord.length()*math.sin(coord.angle()+math.pi/2)
        )

# 點類別
class Point(object):
    # 起始方法
    def __init__(self, x, y):
        self.x = x
        self.y = y

    # 繪製方法
    def drawMe(self, g, r):
        self.g = g
        self.r = r
        self.g.save()
        self.g.moveTo(self.x,self.y)
        self.g.beginPath()
        # 根據 r 半徑繪製一個圓代表點的所在位置
        self.g.arc(self.x, self.y, self.r, 0, 2*math.pi, True)
        self.g.moveTo(self.x,self.y)
        self.g.lineTo(self.x+self.r, self.y)
        self.g.moveTo(self.x, self.y)
        self.g.lineTo(self.x-self.r, self.y)
        self.g.moveTo(self.x, self.y)
        self.g.lineTo(self.x, self.y+self.r)
        self.g.moveTo(self.x, self.y)
        self.g.lineTo(self.x, self.y-self.r)
        self.g.restore()
        self.g.stroke()

    # 加入 Eq 方法
    def Eq(self, pt):
        self.x = pt.x
        self.y = pt.y

    # 加入 setPoint 方法
    def setPoint(self, px, py):
        self.x = px
        self.y = py

    # 加上 distance(pt) 方法, 計算點到 pt 的距離
    def distance(self, pt):
        self.pt = pt
        x = self.x - self.pt.x
        y = self.y - self.pt.y
        return math.sqrt(x * x + y * y)

    # 利用文字標示點的座標位置
    def tag(self, g):
        self.g = g
        self.g.beginPath()
        self.g.fillText("%d, %d"%(self.x, self.y),self.x, self.y)
        self.g.stroke()


# Line 類別物件
class Line(object):

    # 起始方法
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2
        # 直線的第一點, 設為線尾
        self.Tail = self.p1
        # 直線組成的第二點, 設為線頭
        self.Head = self.p2
        # 直線的長度屬性
        self.length = math.sqrt(math.pow(self.p2.x-self.p1.x, 2)+math.pow(self.p2.y-self.p1.y,2))

    # setPP 以指定頭尾座標點來定義直線
    def setPP(self, p1, p2):
        self.p1 = p1
        self.p2 = p2
        self.Tail = self.p1
        self.Head = self.p2
        self.length = math.sqrt(math.pow(self.p2.x-self.p1.x, 2)+math.pow(self.p2.y-self.p1.y,2))

    # setRT 方法 for Line, 應該已經確定 Tail 點, 然後以 r, t 作為設定 Head 的參考
    def setRT(self, r, t):
        self.r = r
        self.t = t
        x = self.r * math.cos(self.t)
        y = self.r * math.sin(self.t)
        self.Tail.Eq(self.p1)
        self.Head.setPoint(self.Tail.x + x,self.Tail.y + y)

    # getR 方法 for Line
    def getR(self):
        # x 分量與 y 分量
        x = self.p1.x - self.p2.x
        y = self.p1.y - self.p2.y
        return math.sqrt(x * x + y * y)

    # 根據定義 atan2(y,x), 表示 (x,y) 與 正 x 軸之間的夾角, 介於 pi 與 -pi 間
    def getT(self):
        x = self.p2.x - self.p1.x
        y = self.p2.y - self.p1.y
        if (math.fabs(x) < math.pow(10,-100)):
            if(y < 0.0):
                return (-math.pi/2)
            else:
                return (math.pi/2)
        else:
            return math.atan2(y, x)

    # setTail 方法 for Line
    def setTail(self, pt):
        self.pt = pt
        self.Tail.Eq(pt)
        self.Head.setPoint(self.pt.x + self.x, self.pt.y + self.y)

    # getHead 方法 for Line
    def getHead(self):
        return self.Head

    def getTail(self):
        return self.Tail

    def drawMe(self, g):
        self.g = g
        self.g.beginPath()
        self.g.moveTo(self.p1.x,self.p1.y)
        self.g.lineTo(self.p2.x,self.p2.y)
        self.g.stroke()

    def test(self):
        return ("this is pure test to Inherit")


class Link(Line):
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2
        self.length = math.sqrt(math.pow((self.p2.x - self.p1.x), 2) + math.pow((self.p2.y - self.p1.y), 2))

    #g context
    def drawMe(self, g):
        self.g = g
        hole = 5
        radius = 10
        length = self.getR()
        # alert(length)
        # 儲存先前的繪圖狀態
        self.g.save()
        self.g.translate(self.p1.x,self.p1.y)
        #alert(str(self.p1.x)+","+str(self.p1.y))
        #self.g.rotate(-((math.pi/2)-self.getT()))
        self.g.rotate(-math.pi*0.5 + self.getT())
        #alert(str(self.getT()))
        #self.g.rotate(10*math.pi/180)
        #this.g.rotate(-(Math.PI/2-this.getT()));
        # 必須配合畫在 y 軸上的 Link, 進行座標轉換, 也可以改為畫在 x 軸上...
        self.g.beginPath()
        self.g.moveTo(0,0)
        self.g.arc(0, 0, hole, 0, 2*math.pi, True)
        self.g.stroke()
        self.g.moveTo(0,length)
        self.g.beginPath()
        self.g.arc(0,length, hole, 0, 2*math.pi, True)
        self.g.stroke()
        self.g.moveTo(0,0)
        self.g.beginPath()
        self.g.arc(0,0, radius, 0, math.pi, True)
        self.g.moveTo(0+radius,0)
        self.g.lineTo(0+radius,0+length)
        self.g.stroke()
        self.g.moveTo(0,0+length)
        self.g.beginPath()
        self.g.arc(0, 0+length, radius, math.pi, 0, True)
        self.g.moveTo(0-radius,0+length)
        self.g.lineTo(0-radius,0)
        self.g.stroke()
        self.g.restore()
        '''
        self.g.beginPath()
        self.g.fillStyle = "red"
        self.g.font = "bold 18px sans-serif"
        self.g.fillText("%d, %d"%(self.p2.x, self.p2.y),self.p2.x, self.p2.y)
        self.g.stroke()
        '''


class Triangle(object):
    def __init__(self, p1, p2, p3):
        self.p1 = p1
        self.p2 = p2
        self.p3 = p3

    def getLenp3(self):
        p1 = self.p1
        ret = p1.distance(self.p2)
        return ret

    def getLenp1(self):
        p2 = self.p2
        ret = p2.distance(self.p3)
        return ret

    def getLenp2(self):
        p1 = self.p1
        ret = p1.distance(self.p3)
        return ret

    # 角度
    def getAp1(self):
        ret = math.acos(((self.getLenp2() * self.getLenp2() + self.getLenp3() * self.getLenp3()) - self.getLenp1() * self.getLenp1()) / (2* self.getLenp2() * self.getLenp3()))
        return ret

    #
    def getAp2(self):
        ret =math.acos(((self.getLenp1() * self.getLenp1() + self.getLenp3() * self.getLenp3()) - self.getLenp2() * self.getLenp2()) / (2* self.getLenp1() * self.getLenp3()))
        return ret

    def getAp3(self):
        ret = math.acos(((self.getLenp1() * self.getLenp1() + self.getLenp2() * self.getLenp2()) - self.getLenp3() * self.getLenp3()) / (2* self.getLenp1() * self.getLenp2()))
        return ret

    def drawMe(self, g):
        self.g = g
        r = 5
        # 繪出三個頂點
        self.p1.drawMe(self.g,r)
        self.p2.drawMe(self.g,r)
        self.p3.drawMe(self.g,r)
        line1 = Line(self.p1,self.p2)
        line2 = Line(self.p1,self.p3)
        line3 = Line(self.p2,self.p3)
        # 繪出三邊線
        line1.drawMe(self.g)
        line2.drawMe(self.g)
        line3.drawMe(self.g)

    # ends Triangle def
    # 透過三個邊長定義三角形
    def setSSS(self, lenp3, lenp1, lenp2):
        self.lenp3 = lenmidpt = Point(0, 0)
        self.lenp1 = lenp1
        self.lenp2 = lenp2
        self.ap1 = math.acos(((self.lenp2 * self.lenp2 + self.lenp3 * self.lenp3) - self.lenp1 * self.lenp1) / (2* self.lenp2 * self.lenp3))
        self.ap2 = math.acos(((self.lenp1 * self.lenp1 + self.lenp3 * self.lenp3) - self.lenp2 * self.lenp2) / (2* self.lenp1 * self.lenp3))
        self.ap3 = math.acos(((self.lenp1 * self.lenp1 + self.lenp2 * self.lenp2) - self.lenp3 * self.lenp3) / (2* self.lenp1 * self.lenp2))

    # 透過兩個邊長與夾角定義三角形
    def setSAS(self, lenp3, ap2, lenp1):
        self.lenp3 = lenp3
        self.ap2 = ap2
        self.lenp1 = lenp1
        self.lenp2 = math.sqrt((self.lenp3 * self.lenp3 + self.lenp1 * self.lenp1) - 2* self.lenp3 * self.lenp1 * math.cos(self.ap2))
        #等於 SSS(AB, BC, CA)

    def setSaSS(self, lenp2, lenp3, lenp1):
        self.lenp2 = lenp2
        self.lenp3 = lenp3
        self.lenp1 = lenp1
        if(self.lenp1 > (self.lenp2 + self.lenp3)):
        #<CAB 夾角為 180 度, 三點共線且 A 介於 BC 之間
            ret = math.pi
        else :
            # <CAB 夾角為 0, 三點共線且 A 不在 BC 之間
            if((self.lenp1 < (self.lenp2 - self.lenp3)) or (self.lenp1 < (self.lenp3 - self.lenp2))):
                ret = 0.0
            else :
            # 透過餘絃定理求出夾角 <CAB 
                ret = math.acos(((self.lenp2 * self.lenp2 + self.lenp3 * self.lenp3) - self.lenp1 * self.lenp1) / (2 * self.lenp2 * self.lenp3))
        return ret

    # 取得三角形的三個邊長值
    def getSSS(self):
        temp = []
        temp.append( self.getLenp1() )
        temp.append( self.getLenp2() )
        temp.append( self.getLenp3() )
        return temp

    # 取得三角形的三個角度值
    def getAAA(self):
        temp = []
        temp.append( self.getAp1() )
        temp.append( self.getAp2() )
        temp.append( self.getAp3() )
        return temp

    # 取得三角形的三個角度與三個邊長
    def getASASAS(self):
        temp = []
        temp.append(self.getAp1())
        temp.append(self.getLenp1())
        temp.append(self.getAp2())
        temp.append(self.getLenp2())
        temp.append(self.getAp3())
        temp.append(self.getLenp3())
        return temp
    #2P 2L return mid P
    def setPPSS(self, p1, p3, lenp1, lenp3):
        temp = []
        self.p1 = p1
        self.p3 = p3
        self.lenp1 = lenp1
        self.lenp3 = lenp3

        #bp3 is the angle beside p3 point, cp3 is the angle for line23, p2 is the output
        line31 = Line(p3, p1)
        self.lenp2 = line31.getR()
        #self.lenp2 = self.p3.distance(self.p1)
        #這裡是求角3
        ap3 = math.acos(((self.lenp1 * self.lenp1 + self.lenp2 * self.lenp2) - self.lenp3 * self.lenp3) / (2 * self.lenp1 * self.lenp2))
        #ap3 = math.acos(((self.lenp1 * self.lenp1 + self.lenp3 * self.lenp3) - self.lenp2 * self.lenp2) / (2 * self.lenp1 * self.lenp3))
        bp3 = line31.getT()
        cp3 = bp3 - ap3
        temp.append(p3.x + self.lenp1*math.cos(cp3))#p2.x
        temp.append(p3.y + self.lenp1*math.sin(cp3))#p2.y
        return temp

def tag(g, p):
    None

midpt = Point(0, 0)
tippt = Point(0, 0)
contour = []
# 執行繪圖流程, 注意 x, y 為 global variables
def draw():
    global theta, midpt, oldpt
    context.clearRect(0, 0, canvas.width, canvas.height)
    line1.drawMe(context)
    line2.drawMe(context)
    line3.drawMe(context)
    #triangle1.drawMe(context)
    #triangle2.drawMe(context)
    theta += dx
    p2.x = p1.x + line1.length*math.cos(theta*degree)
    p2.y = p1.y - line1.length*math.sin(theta*degree)
    p3.x, p3.y = triangle2.setPPSS(p2,p4,link2_len,link3_len)
    # 計算垂直單位向量
    a = Coord(p3.x, p3.y)
    b = Coord(p2.x, p2.y)
    normal = perpendicular(normalize(a-b))
    midpt.x = (p2.x + p3.x)/2
    midpt.y = (p2.y + p3.y)/2
    tippt.x = midpt.x + 150*normal.x
    tippt.y = midpt.y + 150*normal.y
    if theta < 360:
        contour.append((tippt.x, tippt.y))
    context.beginPath()
    context.moveTo(midpt.x, midpt.y)
    context.lineTo(tippt.x, tippt.y)
    # 利用 fillRect 繪製一個長寬各 1 單位的正方形
    for i in range(len(contour)):
        context.fillRect(contour[i][0], contour[i][1], 1, 1)
    context.stroke()
    #p1.tag(context)


# 以上為相關函式物件的定義區
# 全域變數
# 幾何位置輸入變數
x=10
y=10
r=10

# 畫布與繪圖內容
# 其他輸入變數
theta = 0
degree = math.pi/180.0
dx = 2
dy = 4

#set p1.p2.p3.p4 position
lift = 10
p1 =  Point(150,100+lift)
p2 =  Point(150,200+lift)
p3 =  Point(300,300+lift)
p4 =  Point(350,100+lift)

#accord position create link
line1 =  Link(p1,p2)
line2 =  Link(p2,p3)
line3 =  Link(p3,p4)
line4 =  Link(p1,p4)
line5 =  Link(p2,p4)

link2_len = p2.distance(p3)
link3_len = p3.distance(p4)

#link2_len = line1.getR()
#link3_len = line3.getR()
#alert(str(link2_len)+','+str(link3_len))

triangle1 =  Triangle(p1,p2,p4)
triangle2 =  Triangle(p2,p3,p4)

# 視窗載入時執行內容
# 繪圖畫布設定

canvas = document["plotarea"]
context = canvas.getContext("2d")

# 座標轉換, 移動 canvas.height 並且 y 座標變號, 也就是將原點座標移到畫面左下角
context.translate(0,canvas.height)
context.scale(1,-1)

#以間隔 20 micro seconds 重複呼叫 draw()
timer.set_interval(draw,20)
#timer.set_interval(draw,10)

fourbar2.py

from math import pi, cos, sin, sqrt, acos
 
radian = 180/pi
degree = pi/180

#PLAP
def plap(ax, ay, ac, bac, bx, by, pos):
    if pos == 0:
        cx= ac*cos(bac - acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ax 
        cy= ac*sin(bac - acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ay
    else:
        cx= ac*cos(bac + acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ax 
        cy= ac*sin(bac + acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ay
    return cx, cy
    
#PLLP
def pllp(ax, ay, ac, cb, bx, by, pos):
    if pos == 0:
        cx =  -((ay - by)*(-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 - sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx)) + (ac**2 - ax**2 - ay**2 + bx**2 + by**2 - cb**2)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))/(2*(ax - bx)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
        cy =  (-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(-ax + bx))/(2*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
    else:
        cx =  -((ay - by)*(-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx)) + (ac**2 - ax**2 - ay**2 + bx**2 + by**2 - cb**2)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))/(2*(ax - bx)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
        cy =  (-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx))/(2*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
    return cx, cy
    
class fourbar(object):

    '''
    (ax, ay) motor coord
    (bx, by) rocker base coord
    bac motor angle
    ac link1 length
    cd link2 length
    db link3 length
    ce triangle side1
    ed triangle side2
    '''
    def __init__(self, ax, ay, bx, by, bac, ac, cd, db, ce, ed):

        self.ax = ax
        self.ay = ay
        self.bx = bx
        self.by = by
        self.bac = bac
        self.ac = ac
        self.cd = cd
        self.db = db
        self.ce = ce
        self.ed = ed
        
    @property
    def cx(self):
        return plap(self.ax, self.ay, self.ac, self.bac, self.bx, self.by, pos=0)[0]

    @property
    def cy(self):
        return plap(self.ax, self.ay, self.ac, self.bac, self.bx, self.by, pos=0)[1]

    @property
    def dx(self):
        return pllp(self.cx, self.cy, self.cd, self.db, self.bx, self.by, pos=0)[0]

    @property
    def dy(self):
        return pllp(self.cx, self.cy, self.cd, self.db, self.bx, self.by, pos=0)[1]
        
    @property
    def ex(self):
        return pllp(self.cx, self.cy, self.ce, self.ed, self.dx, self.dy, pos=0)[0]

    @property
    def ey(self):
        return pllp(self.cx, self.cy, self.ce, self.ed, self.dx, self.dy, pos=0)[1]

'''    
# 利用 fourbar 物件建立案例
f = fourbar(ax = -60, ay = 0, bx = 0, by = 0, bac = 50*degree, ac = 30, cd = 50, db = 60, ce = 50, ed = 50)

# 利用 fourbar 物件案例的方法求各點座標
#f.cx, f.cy 為 C 點座標
#f.dx, f.dy 為 D 點座標
#f.ex, f.ey 為 E 點座標
'''

plap_pllp.py

# http://mde.tw/cp2018/content/Pyslvs%20%E7%AF%84%E4%BE%8B.html
# http://mde.tw/cp2018/downloads/2014_nsysu_design_linkage_type_foot_exercise_machine.pdf
# http://mde.tw/cp2018/blog/2018-Fall-Python-Getting-Started.html
# triangle_fourbar_point_track.py
from math import pi, cos, sin, sqrt, acos
import matplotlib.pyplot as plt
  
radian = 180/pi
degree = pi/180
  
#PLAP
def plap(ax, ay, ac, bac, bx, by, pos):
    if pos == 0:
        cx= ac*cos(bac - acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ax 
        cy= ac*sin(bac - acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ay
    else:
        cx= ac*cos(bac + acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ax 
        cy= ac*sin(bac + acos((ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 + abs(ax - bx)**2 - abs(ay - by)**2)/(2*sqrt(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2)*abs(ax - bx)))) + ay
    return cx, cy
  
#PLLP
def pllp(ax, ay, ac, cb, bx, by, pos):
    if pos == 0:
        cx =  -((ay - by)*(-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 - sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx)) + (ac**2 - ax**2 - ay**2 + bx**2 + by**2 - cb**2)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))/(2*(ax - bx)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
        cy =  (-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(-ax + bx))/(2*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
    else:
        cx =  -((ay - by)*(-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx)) + (ac**2 - ax**2 - ay**2 + bx**2 + by**2 - cb**2)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))/(2*(ax - bx)*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
        cy =  (-ac**2*ay + ac**2*by + ax**2*ay + ax**2*by - 2*ax*ay*bx - 2*ax*bx*by + ay**3 - ay**2*by + ay*bx**2 - ay*by**2 + ay*cb**2 + bx**2*by + by**3 - by*cb**2 + sqrt((-ac**2 + 2*ac*cb + ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2 - cb**2)*(ac**2 + 2*ac*cb - ax**2 + 2*ax*bx - ay**2 + 2*ay*by - bx**2 - by**2 + cb**2))*(ax - bx))/(2*(ax**2 - 2*ax*bx + ay**2 - 2*ay*by + bx**2 + by**2))
    return cx, cy
 
def crank_rocker(angle, p1x, p1y, p2x, p2y, len1, len2, len3, len4, len5):
    p4x, p4y = plap(p1x, p1y, len1, angle, p2x, p2y, 0)
    #print("cx=", cx, "cy=", cy)
    p5x, p5y = pllp(p4x, p4y, len2, len3, p2x, p2y, 0)
    #print("dx=", dx, "dy=", dy)
    p3x, p3y = pllp(p4x, p4y, len4, len5, p5x, p5y, 0)
    #print("ex=", ex, "ey=", ey)
    return p3x, p3y
     
#主程式
Xval  = []
Yval  = []
inc = 5
 
for i in range(0, 360+inc, inc):
    try:
        p3x, p3y = crank_rocker(i*degree, 0, 0, 90, 0, 35, 70, 70, 40, 40)
        Xval += [p3x]
        Yval += [p3y]
        print(i, ":", round(p3x, 4), round(p3y, 4))
    except:
        pass
print ("Solve Completed")
 
plt.plot(Xval, Yval)
plt.xlabel('x coordinate')
plt.ylabel('y coordinate')
#plt.title("Involute - "+str(degree)+" deg")
plt.show()

read_csv_draw_line.py

from browser import document as doc
from browser import html
import math
# 準備繪圖畫布
canvas = doc["fourbar"]
container1 = doc['container1']
ctx = canvas.getContext("2d")

fourbar_data = open("./../w7/11117.csv").read()
fourbar_list = fourbar_data.splitlines()
#container1 <= fourbar_list[0]
# 以下可以利用 ctx 物件進行畫圖
# 先畫一條直線
ctx.beginPath()
# 設定線的寬度為 1 個單位
ctx.lineWidth = 1
# 利用 transform 將 y 座標反轉, 且 offset canvas.height
# (X scale, X skew, Y skew, Y scale, X offset, Y offset)
# 配合圖形位置進行座標轉換
ctx.transform(1, 0, 0, -1, canvas.width/2+250, canvas.height/2+100)
# 畫出 x 與 y 座標線
# 各座標值放大 8 倍
ratio = 8
'''
ctx.moveTo(0, 0)
ctx.lineTo(0, 100)
ctx.moveTo(0, 0)
ctx.lineTo(100, 0)
'''
ctx.moveTo(0, 0)
ctx.lineTo(-30*ratio, 0)
start_point = fourbar_list[0].split(",")
ctx.moveTo(float(start_point[0])*ratio, float(start_point[1])*ratio)
count = 0
for data in fourbar_list[1:]:
    point = data.split(",")
    #count = count + 1
    #container1 <= str(count) + ":" + point[0] + "," + point[1]
    #container1 <= html.BR()
    ctx.lineTo(float(point[0])*ratio, float(point[1])*ratio)
# 設定顏色為藍色, 也可以使用 "rgb(0, 0, 255)" 字串設定顏色值
ctx.strokeStyle = "blue"
# 實際執行畫線
ctx.stroke()
ctx.closePath()