| The transformation matrix method is extended to investigate how a dimensional error affects the operation of a mechanical system. The new method is implemented into the already existing Integrated Mechanisms Program (IMP), which had not yet had the features of error analysis.; The characteristics of interest in a mechanism, such as position and velocity, are approximated by expanding each function in a first order Taylor series. In order to estimate the output characteristics of the system using this approach, it is necessary to determine the partial derivatives of the output characteristics of the system with respect to a small deformation in a part. These derivative values are derived from the loop closure equation of the mechanism by differentiating the loop equation with respect to the small deformation. The advantage of this approach is that it is applicable to very complex problems for which such a functional relationship is not otherwise available.; With regard to force analysis, dynamic equations are developed in RAP from Lagrange's equation of motion. These equations have been used to study the dynamic forces and moments in the joints of a mechanism under the effect of a dimensional error in a mechanical part. To estimate the resulting change in the force and moment requires knowledge of the partial derivatives of various kinds of forces produced in the system such as the dynamic force from the inertia of moving links, the gravity effect and any external forces acting on the links.; After the technique was developed, subprograms were written and added into IMP to demonstrate the feasibility of the ideas on selected example problems. This method now makes it possible to simulate and analyze a mechanism whose parts may have an error in shape. Thus, this allows the design engineer to analyze a problem even when it does not function correctly, and to make an early discovery of what part may cause the mechanism to perform erroneously. |
