Graphical Synthesis of Cam Mechanisms,5-3 Plate Cam with Translating Roller (or Knife-edge) Follower,5.4 Plate Cam with Oscillating Roller Follower（摆动滚子从动件圆盘凸轮）,5.5 Plate Cam with Translating Flat-faced Follower (直动平底从动件圆盘凸轮）,5-3 Plate Cam with Translating Roller (or Knife-edge) Follower,Graphical methods offer clear physical concepts and can help us to understand the analytical methods,1. A plate cam with translating offset knife-edge follower(偏心尖底直动从动件圆盘凸轮） is to be designed to accomplish(完成) a motion as follows:,h=80mm, o =140, o=100, S =40, S= 80, e=40mm; rise with 3-4-5 polynomial(多项式) motion curve; return with sine acceleration motion curve; The cam rotates counter-clockwise; The minimum radius rP of the cam is 100mm.,At first: calculate the displacement S of the follower for different values of the cam angle according to the given motion curve.,For the return,For the rise,If the cam rotates an angle B0OB= counter-clockwise from the beginning, the follower will rise through a corresponding distance BB=S from the lowest position along its guide way.,Suppose that the cam mechanism has been designed according the given motion curve S-.,Cam Rotating,Follower Rotating,Therefore, motion curve S- can be understood such ways: The cam is stationary. The frame and the follower rotate in the direction opposite to .,The follower will rise through a corres-ponding S along the guide-way relative to the frame. This is the principle of inversion(反转法).,During inversion, the extension of the follower guide-way always stays tangent to a circle with radius equal to the offset e and centred at the centre O of the camshaft.,This circle is called the offset circle(偏置圆).,During inversion, the locus traced by the knife-edge is the cam contour, which is also called the pitch curve(理论廓线).,The minimum circle centred at O and tangent to the pitch circle is called the base circle of the cam pitch curve, or prime circle(基圆).,The procedure(步骤) to design the pitch curve:,Note: (1) The pitch curve can not be drawn in the direction of .,(2) The point B can not be located by laying off BB=S along OB.,(3) The centre line of the follower is always tangent to the offset circle.,If offset e=0, the offset translating follower becomes an in-line translating follower.,What will happen if e=0?,Characteristics: The roller is always tangent to the cam contour(实际廓线) at all times.,2. Graphical Synthesis of Plate Cam with Translating Roller Follower （直动滚子从动件圆盘凸轮）,The locus of the roller centre relative to the cam is called the pitch curve(理论廓线） of the cam. The roller is tangent to the cam contour(实际廓线) at all times, and the cam contour is the envelope(包络线）of the family of the roller circles.,The pitch curve (理论廓线) and the cam contour (实际廓线) are parallel(法向等距). The minimum radius of the pitch curve is called the radius rP of the prime circle. Note: the minimum radius of the cam contour is not rP.,For the knife-edge follower, the pitch curve and the cam contour are the same.,Suppose： A virtual(虚拟的) translating knife-edge follower is welded(焊) to the translating roller follower The knife-edge coincides(重合) with the roller centre. The locus of the knife-edge, or the locus of the roller centre, or pitch curve, relative to the cam can be designed.,The process to design the cam contour is:,5.4 Plate Cam with Oscillating Roller Follower（摆动滚子从动件圆盘凸轮）,In this mechanism, The angular lift(角行程) of the follower is max. The motion equations can also apply to the oscillating follower so long as S is replaced by and h by max,The cam contour is obtained by drawing a smooth curve tangent to the family of all roller circles.,Since the follower arm must have some physical dimensions, the side edge of the straight arm of the follower may interfere(干涉) with the cam contour. It is necessary to check that this will not occur at all positions. To avoid interference, the arm may be designed as a bent(弯曲) rod.,5.5 Plate Cam with Translating Flat-faced Follower (直动平底从动件圆盘凸轮）,This follower is used often in high-speed cam mechanisms. The motion curve of the follower will be restricted since all sections of the cam contour must be convex（凸起）.,Inline? Offset？ Redundant constraint,The cam contour may be drawn as a smooth curve tangent to the family of the position lines of the flat face.,Graphical Synthesis of Cam Mechanisms,5-3 Plate Cam with Translating Roller (or Knife-edge) Follower,5.4 Plate Cam with Oscillating Roller Follower（摆动滚子从动件圆盘凸轮）,5.5 Plate Cam with Translating Flat-faced Follower (直动平底从动件圆盘凸轮）,(1) Analytical Synthesis of the Pitch Curve Lead to a substantial(显著的) saving of time in the design process.,5.6 A Few Questions Should Be Discussed,(2) Pressure Angle,(3) The minimum radius of the prime circle (最小基圆半径),Pressure Angle,Pressure angle changes during motion so it is necessary to control the value of the maximum pressure angle max.,pressure angle Return in Return in form-closed force-clo