机械原理大作业平面连杆机构报告

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平面连杆机构的运动分析

（题号：平面六杆机构）

一、题目说明

图示为一平面六杆机构。设已知各构件的尺寸如表1所示，又知原动件1以等角速度??1=1rad/s沿逆时针方向回转，试求各从动件的角位移、角速度及角加速度以及E点的位移、速度及加速度的变化状况。

已知其尺寸参数如下表所示：

组号l1l2l3l4l5l6αABC2-A2-B26.567.587.552.443.02-C600l2=116.6l2=111.6l2=126.6

二、题目分析

1、建立封闭图形：

L1+L2=L3+L4

L1+L2=L5+L6+AG

2、机构运动分析：

a、角位移分析

由图形封闭性得：

L1?cos?1?L2?cos?2?L3?cos?3?L4??L1?sin?1?L2?sin?2?L3?sin?3??'L?cos??L?cos??L?????2)?xG?L6?cos?6?L5?cos?51222?cos(?1'?L?sin??L?sin??L11222?sin(?????2)?yG?L6?sin?6?L5?sin?5?将上式化简可得：

L2?cos?2?L3?cos?3?L4?L1?cos?1??L2?sin?2?L3?sin?3??L1?sin?1??'L?cos??L?2??)?L5?cos?5?L6?cos?6?xG?L432?cos(?3'?L?sin??L?2??)?L5?sin?5?L6?sin?6?yG332?sin(?

b、角速度分析

上式对时间求一阶导数，可得速度方程：

化为矩阵形式为：

?L2?sin?2??2?L3?sin?3??3?L1?sin?1??1??L2?cos?2??2?L3?cos?3??3??L1?cos?1??1??'?L?sin????L?2??)??2?L5?sin?5??5?L6?sin?6??6?0332?sin(?3'?L?cos????L?2??)??2?L5?cos?5??5?L6?cos?6??6?0332?cos(?3

??L2?sin?2?L?cos?22???L'2?sin(?2??)?'?L2?cos(?2??)?L1?sin?1???L?cos??1???1??1??0??0??L3?sin?3?L3?cos?3?L3?sin?3L3?cos?300?L5?sin?5L5?cos?5???2?????0???3?L6?sin?6???5?????L6?cos?6???6?0

c、角加速度分析：

矩阵对时间求一阶导数，可得加速度矩阵

??L2?sin?2?L?cos?22???L'2?sin(?2??)?'?L2?cos(?2??)??L2?cos?2??L?sin?22?'?L2?cos(?2??)?'?L2?sin(?2??)???2??????L3?cos?300???3???L3?sin?3?L5?sin?5L6?sin?6???5????L3?cos?3L5?cos?5?L6?cos?6???6?2L3?cos?300??L?cos???2?11???2??L?sin??L3?sin?300?1????3???2??11??L3?cos?3L5?cos?5?L6?cos?6???52?0??2???L3?sin?3L5?sin?5?L6?sin?6??0?????6?00L3?sin?3

d、E点的运动状态

?xE?xG?L6?cos?6?L5?cos?5位移：?y?y?L?sin??L?sin?

G6655?E??vEx??L6?sin?6??6?L5?sin?5??5速度：?v?L?cos????L?cos????E666555?y加速度：

22?a??L?cos????L?sin????L?cos????Ex666666555?L5?sin?5??5?22a??L?sin????L?cos????L?sin????L5?cos?5??5?E666666555?y

三、流程图

{

doublexe,ye,A,B,C,phi,alpha,csn,ang5g,d2,d,ang2,ang3,ang5,ang6;A=2*l1*l3*sin(ang1);B=2*l3*(l1*cos(ang1)-l4);

C=l2*l2-l1*l1-l3*l3-l4*l4+2*l1*l4*cos(ang1);ang3=2*atan((A+sqrt(A*A+B*B-C*C))/(B-C));if(ang32*PI)value[i]-=2*PI;while(value[i]

xe178.818179.925179.397177.642174.992171.677167.862163.678159.245154.681150.103145.621141.343137.36133.75130.574127.871125.663123.955122.737121.992121.704121.861122.467123.543125.136127.319130.188133.853138.412143.915150.292157.279164.354170.77175.756

yevexveyaexaey27.07211.761-39.671-65.17650.7621.0491.265-28.775-53.89670.23117.111-6.912-16.411-40.0268.52315.229-12.885-5.559-29.07454.70315.007-17.2672.525-21.62237.98715.947-20.567.817-16.36123.15117.601-23.03410.801-12.09311.6119.617-24.812.058-8.1583.29821.74-25.88612.111-4.295-2.27123.8-26.30111.395-0.475-5.60925.693-26.05910.2583.224-7.14827.373-25.198.9836.676-7.24828.834-23.7517.7939.745-6.22430.108-21.8186.85912.31-4.37131.25-19.4896.29914.279-1.97632.333-16.8716.18415.6050.67533.436-14.0796.53316.2963.30234.639-11.2167.3216.4235.64536.013-8.3718.47416.1147.47837.612-5.6069.8915.5558.62239.472-2.94311.43714.9678.95641.603-0.36912.96514.5888.40543.9882.17514.31714.6546.93146.5814.78415.32915.3744.50349.3097.58815.8316.9011.06952.06710.73515.63719.301-3.48354.71514.37214.53922.491-9.3457.07418.61312.28526.139-16.76858.91923.4828.57929.51-26.0359.96528.8213.0931.257-37.15359.87734.175-4.45929.25-49.40558.28638.654-14.08820.76-60.39754.87240.91-25.1833.568-65.13349.50739.43-36.038-21.485-56.41742.47333.327-43.773-47.791-29.08534.5923.312-45.351-64.53912.208图像

角位移

角速度

角加速度

E点的位移、速度及加速度

六、体会及建议：

这次的