【正文】 The diagram below shows how to to construct a vector diagram for the acceleration ponents on a s。 1) the centripetal ponent due to the angular velocity of the relative to A = perpendicular to the line. The velocity of B relative to B39。 The velocity of P is obtained from the vector diagram by using the relationship bp/bc = BP/BC The velocity vector diagram is easily drawn as shown... Velocity of sliding Block on Rotating LinkConsider a block B sliding on a link rotating about A. The block is instantaneously located at B39。 The velocity of C relative to B is perpedicular to CB and passes through b As A and D are fixed then the velocity of D relative to A = 0 a and d are located at the same point If three position of the output lever are required corresponding to the angular position of the input lever at three positions then this equation can be used to determine the appropriate lever lengths using three simultaneous equations... Velocity Vectors for LinksThe velocity of one point on a link must be perpendicular to the axis of the link, otherwise there would be a change in length of the link.On the link shown below B has a velocity of vAB = perpendicular to AB. K3 = ( l 32 l 12 l 22 l 2 4 ) / 2 l 2 l 4 This equation enables the analytic synthesis of a 4 bar linkage. K2 = l 1 / l 2s Equation results from this relationship as K 1 cos θ 2 + K2 cos θ 4 + K 3 = cos ( θ 2 θ 4 )K1 = l1 / l4 The system has no toggle positions and the linkage is a poor design Freudenstein39。When using four bar linkages to transfer torque it is generally considered prudent to avoid transmission angles below 450 and 500.In the figure above if link (d) is made the driver the system shown is in a locked position. In these region the linkage is very liable to lock up with very small amounts of friction. As the value sin(transmission angle) bees small the mechanical advantage of the linkage approaches zero. These positions allow the 4 bar linkage to be used a clamping tools.The angle β is called the transmission angle.These positions are referred to as toggle positions. These angles are not constant so it is clear that the mechanical advantage is constantly changing.The linkage positions shown below with an angle α = 0 o and 180 o has a near infinite mechanical advantage. It can be proved that the mechanical advantage is directly proportional to Sin( β ) the angle between the coupler link(c) and the driven link(d), and is inversely proportional to sin( α ) the angle between the driver link (b) and the coupler (c) .s law states that one of the links (generally the shortest link) will be able to rotate continuously if the following condition is met... b (shortest link ) + c(longest link) a + dFour Inversions of a typical Four Bar LinkageNote: If the above condition was not met then only rocking motion would be possible for any link..Mechanical Advantage of 4 bar linkageThe mechanical advantage of a linkage is the ratio of the output torque exerted by the driven link to the required input torque at the driver link.s law provides a simple test for this conditionGrashof39。 One link is always fixed so before any joints are attached the number of degrees of freedom of a linkage assembly with n links = DOF = 3 (n1) Connecting two links using a joint which has only on degree of freedom adds two constraints. Connecting two links with a joint which has two degrees of freedom include 1 restraint to the systems. The number of 1 DOF joints = say j 1 and the number of joints with two degrees of freedom = say j 2.. The Mobility of a system is therefore expressed as mobility = m = 3 (n1) 2 j 1 j 2Examples linkages showing the mobility are shown below.. A system with a mobility of 0 is a structure. A system with a mobility of 1 can be fixed in position my positioning only one link. A system with a mobility of 2 requires two links to be positioned to fix the linkage position..This rule is general in nature and there are exceptions but it can provide a very useful initial guide as the the mobility of an arrangement of links...Grashof39。It is possible to determine this from the number of links and the number and types of joints which connect the links...A free planar link generally has 3 degrees of freedom (x , y, θ ). The mobility of a linkage is the number of input parameters which must be controlled independently in order to bring the device to a set position.The motions of all of the particles in the mechanism are concentric and can be repesented by their shadow on a spherical surface which is centered on the mon location..Spherical mechanisms /linkages are not considered on this pageMobilityAn important factor is considering a linkage is the mobility expressed as the number of degrees of freedom.Planar mechanisms ultilising only lower pairs are called planar linkages. Planar linkages only involve the use of revolute and prismatic pairsA spatial mechanism has no restrictions on the relative movement of the particles. Planar and spherical mechanisms are subsets of spatial mechanisms..Spatial mechanisms / linkages are not considered on this pageSpherical mechanisms has one point on each linkage which is stationary and the stationary point of all the links is at the same location. Spatial mechanisma are far more plicated to engineer requiring puter synthesis. The majority of linkages and mechanisms are designed as planer systems. The main reason for this is that planar systems are more convenient to engineer. Here, both choosing the types as well as the dimensions of the new mechanism can be part of kinematic synthesis.Planar, Spatial and Spherical MechanismsA planar mechanism is one in which all particles describe plane curves is space and all of the planes are coplanar.. Kinematic synthesis is the process of designing a mechanism to acplish a desired task. These type of connections, revolute and prismatic,