The utilization of robots, for mechanical part assemblies, is a current practice. Existing methods and software permit to simulate tasks and program them off line using the perfect geometry of the parts. However, as the parts to be assembled are never perfect the adjustment time of these programs is often too long. It is indispensable to find models that can integrate these manufacturing uncertainties at the simulation level. The method proposed can replace the verification using manual functional gauges and can be integrated to a simulation software. In relation to the existing methods, it is especially suitable for the intended parts to be assembled and the datum reference frame (DRF) is defined at maximum material condition. This paper proposes a method for all situations of the DRF where the part is in conformance. It can be applied to inspection, as well as to tolerance analysis and synthesis. A kinematic model is used to represent the permissible motion of the DRF.

The paper presented by Gautier and Khalil (see ibid., vol.6, no.3, p.368-73, 1990) gives a direct and efficient method of calculating most of the minimum inertial parameters of serial robots. Some parameters concerning the translational links between the first two rotational joints that are not parallel need particular calculation; partial results concerning the case where these links are either perpendicular or parallel are given in the above paper. This correspondence presents a direct solution of this particular case, such that all the minimum inertial parameters can be obtained directly without calculating the energy or the dynamic model of any link.>

The authors present two methods for determining the base inertial parameters of robots containing closed loops. This set of parameters is the minimum set which can be identified using the dynamic or energy model. The first method is symbolic; the solution is obtained by first determining the quasi base parameters of a corresponding tree structure robot; the closed-loops are then taken into account to get the quasi base parameters of the robot. Direct general relations are given for the two steps. The second method is numerical; the multiple solutions of the relations expressing the passive variables as a function of active variables are taken into account; the number of the base parameters is seen to be a function of each solution.>

A symbolic method to determine the minimum set of inertial parameters of robots containing parallelogram closed loops is presented. The solution is obtained by determining the minimum inertial parameters of an equivalent tree structure. Then, the constraint equations of the closed loops are taken into account to get the global minimum inertial parameters. Direct general relations are obtained for the two steps.>

A symbolic method of determining the minimum set of inertial parameters of robots containing parallelogram closed loops is presented. The solution is obtained by determining the minimum inertial parameters of an equivalent tree structure robot and then taking into account the constraint equations of the closed loops to get the global minimum inertial parameters. Direct general relations that do not require the calculation of the dynamic model of the system are obtained for the two steps. The method is general whatever the values of the geometric parameters.>