Position Analysis of Spherical 4 Bar Mechanisms
Introduction

A spherical four bar linkage is a mechanism whose joints (revolute) lie on the surface of a sphere in any configuration of the mechanism. It consists of 4 links joined in space by revolute joints which allow motoion only on the surface of a sphere. The axes of revolution of the four revolute joints meet at a common point, which is the center of the sphere characterizing such a mechanism. The spherical four bar mechanism is the spatial analog of the planar four bar RRRR mechanism.  In case of the planar mechanism, the link length is the shortest distance between the revolute joints. that form the basis of the linkage. Likewise in case of the spherical linkage, the analog of the length of the link between two joints, is the angular span between  the axis of two revolute joints that the link spans, measured with the centre of the sphere inquestion as the vertex of the angle.

In this case the Grasphof criteria takes the form

l+s<=p+q

Where l,s stand for the longest and shortest angular spans, and p and q for the other two spans. The spherical linkage offers complete rotatability if this criteria is satisfied. Chiang has classified such linkages into two classes

  •  Class 1 linkages are those which satisfy Grashof's rule. They may also be termed as Grashoflinkages. For this class of linkages, the shortest linkis capable of making complete revolutions relative tothe other three links, and
    1. a crank-rocker exists if the link adjacent to the shortest link is fixed
    2. adrag-link exists if the shortest link is fixed
    3.  a double-rocker exists if the link opposite to theshortest link is fixed
  •  Class 2 linkages are those which do not satisfyGrashof's rule. They may also be termed as non-Grashof linkages. For this class of linkages, none ofthe links is capable of making complete revolutionsrelative to the other links, and a double-rocker existswhatever a link is chosen as the frame. The linkageexhibits
    1. internal rocking angles if the fixed hnk isthe longest link
    2. external rocking angles if the coupler is the longest link
    3. overlapping rocking angles if one of the two linksadjacent to the fixed link is the longest link
        

In this experiment you will have to assemble a spherical mechanism by providing the four link angles (in degrees) to the simulator and observe the range of motions and its dependence on the link angles as outlined by Grashof criteria for spherical mechanisms.