The dissertation thesis is used as a methodology for prediction of selected parameters of rotational kinematic pairs of machine tools. The motivation for its writing has been continually increasing requirements for parameters (performance, accuracy, static and dynamic stiffness) of machine tools. The methodology takes into account the availability of suitable measuring devices and description of the design of rotary kinematic pairs. It will be useable for predicting the behavior of rotational kinematic pairs, even at the design stage by applying results to the machine design. The work is processed so that first is used a system approach to suggest methodology for prediction of the behavior of rotary kinematic pair in CNC machine tools, planning measurement strategy and verifying the results, including applications for specific kinematic chain of the selected machine. Based on this system approach and the resulting methodology, the measurement of the rotary kinematic pair was performed. The results of the system approach and measurement are generalized in the form of recommendations for designers of machining centers, allowing to increase the accuracy of the rotational kinematic pair.

The aim of this research is to bridge the gap between CAD modeling and kinematic analysis packages by extracting kinematic information directly from part genometries. It will relieve the designers from the tedious task of specifying assembly constraints and specifying redundant information for creating kinematic models. Automatic generation of kinematic assembly models is achieved by characterizing the lower kinematic pairs: cylindrical, spherical, prismatic, planar and revolute; from the geometries point of view. Based on characterization, the algorithms are developed to recognize these kinematic pairs from a pair of part genometries. The combinations of primitive genometric entities: vertices, edges and faces; forming point, line, arc and surface contacts are studied. The signature geometry is found to be associated with each type of joint. The contacts are analysed for restraining the relative motion between a pair of parts. Based on this, the form closure conditions are derived for surface, line, arc and point contacts for each type of joint. The algorithms are developed to automatically recognize these joints and to assemble them into a kinematic assembly model represented as a graph. The strength and novelty of the present procedure is that kinematic pairs can be recognized for conforming as well as non conforming genometries. A Visual Basic for Application (VBA) for Solid Works has been developed using Application Programming Interface (API) for user interaction. The part genometries can be in any 3D solid modeling neutral file format (.sat, .igs, etc) or some of the native formats of CAD softwares supported by Solid Works. The regions of interest can be directly identified through mouse pick on parts using Solid Works Graphical User Interface (GUI). The transformation matrices are derived automatically to position the parts relative to each other. The local interference between part geometries is also considered for checking the validity of the kinematic pair in the assembly. Assembly model is created and represented as a directed graph. The present implementation, built on the ACIS geometry kernel, imports the parts into SolidWorks, specifies the mating regions using a visual Basic interfaces and finally generates the kinematic assembly model as an ADAMS input file complete with part genometries, their mass properties, kinematic joints and their locations.

The present work studies instantaneous motion of smooth planar and spatial objects in unilateral point contacts. The traditional first-order instantaneous kinematic analysis is found insufficient to explain many common physical scenarios. The present work looks beyond the velocity state of motion for a comprehensive understanding through higher-order kinematic analysis of the above system. The methodology proposed herein is a Euclidean space approach to second-order motion space analysis of objects in point contacts. The geometries of the objects are approximated up to second-order in the differential vicinity of the point of contact; meaning, up to curvature at the point of contact. The instantaneous motion is approximated up to second-order kinematics, i.e., up to acceleration state. The basic approach consists of impressing an instantaneous motion upon one object while holding the other fixed which is in a single point contact initially, and observing for one of the following three states: penetration, separation, and persistence of contact between the two objects. These three states are characterized by the interference between the geometries of the objects. Penetration and separation of two curves for rotation about points on the plane is geometrically studied based on the relative configuration of the osculating circles at the point of contact. It is shown that the plane is partitioned into four regions of rotation centers. Partitioning of the plane into motion space regions at a contact provided a geometrical framework compose the motion space for multiple contacts. The applications include second-order form-closure (SFC) and synthesis of kinematic pairs. To explore the consequence of a generic motion, an analytical scheme is formulated using the screw theoretic concepts of twist and twist-derivative. It is shown that the characteristics of second-order motions at a single contact depends only upon the geometric kinematic properties of the motion; meaning, the motion characteristics are time-independent. The geometric conditions for the second-order motion that will be admissible or restrained at a contact are not available in the existing literature on \second-order mobility". The classical Euler-Savary equation for enveloping curves is found to represent the condition which is both necessary and sufficient for the second-order roll-slide motion. An elegant generalized geometric characterization of second-order motions is derived. This is made use for deriving condition of immobilization of, planar mechanisms with up to 2-degrees-of-freedom (d.o.f.), with a single point contact. Illustrative examples of four-bar and 2R-mechanisms are presented. Rapid prototyped model of the four-bar mechanism is fabricated and the SFC theory is verified satisfactorily. Through a novel use of Meusnier's theorem, rotational motion characteristics of planar curves in a point contact is used to determine the patterns and distribution of admissible axes of rotation in space for two surfaces in a single point contact. In the generalized analytical method of motion space analysis, the surfaces are locally represented in Monge's form up to second-order terms and motion is represented using twist and twist-derivative. An analytical framework for the second-order motion space analysis of surfaces with multiple contacts has been developed. Using this procedure, pairs of objects are analyzed for SFC and equivalent lower kinematic pair freedom. Revolute and planar joints with two contacts, prismatic joint with three contacts, SFC of regular concave spherical tetrahedron and regular tetrahedron with four contacts are demonstrated. Although conventional first-order studies demand seven contact points for form-closure, within the context of second-order motion, the present study established that, under special geometric conditions relative immobilization of two smooth objects can be enabled with much fewer contacts. Conditions for immobilization using three and two smooth contacts have been derived. Using contact kinematics equations based on higher-order reciprocity, an instantaneous spatial higher pair to lower pair substitute-connection which is kinematically equivalent up to acceleration analysis for two smooth surfaces in persistent point contact is derived. An illustrative example of a three-link direct-contact mechanism is presented.