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In a physical 3-dimensional free space at most six degrees of freedom can be independent, i.e. three for position and three for orientation. Intuitively robots with six joints are adequate to execute any tasks. However, in reality, constraints often exist under the complex environment so that six joints are not quite enough for the robots. An insertion of an additional joint into the robot may solve the problems. This paper discusses only the singularity problem at which the robot degenerates. The analysis, which is a continued investigation of a previous study, shows how the degeneracy entrapment could be escaped as rapidly as possible if the robot has seven joints; between which two joints the redundant joint should be inserted; and which type of joint (i.e revolute or prismatic) should be employed.