Spatial Cams Research Articles

The Synthesis of the Axodes of RCCC Linkages

As the coupler link of an RCCC linkage moves, its instant screw axis (ISA) sweeps a ruled surface on the fixed link; by the same token, the ISA describes on the coupler link itself a corresponding ruled surface. These two surfaces are the axodes of the linkage, which roll while sliding and maintaining line contact. The axodes not only help to visualize the motion undergone by the coupler link but also can be machined as spatial cams and replace the four-bar linkage, if the need arises. Reported in this paper is a procedure that allows the synthesis of the axodes of an RCCC linkage. The synthesis of this linkage, in turn, is based on dual algebra and the principle of transference, as applied to a spherical four-bar linkage with the same input–output function as the angular variables of the RCCC linkage. Examples of RCCC linkages are included. Moreover, to illustrate the generality of the synthesis procedure, it is also applied to a spherical linkage, namely, the Hooke joint, and to the Bennett linkage.

4-Axis CNC Machine Tool for Relief Grinding Sphere Gear Hob

A new 4-axis machine tool, which is used for relief grind of sphere gears hob including spherical hob, elliptic hob and arc surface hob, is developed. The principle of relief machining of spherical hob is introduced first. Transmitting system, numerical system and some key techniques are then introduced. The machine tool can be reconfigured in machining of arc worms and spatial cams beside of machining of spherical hob. Four forms of the machine tool for machining different workpiece are also introduced. DOI: http://dx.doi.org/10.11591/telkomnika.v10i7.1557

Design of 4-Axis Reconfigurable CNC Machine Tool for Relief Grinding Sphere Gear Hob

a new 4-axis machine tool, which is used to relief grind sphere gear hob including spherical hob, elliptic hob and arc surface hob, is developed. The principle of machining of spherical hob is introduced first. Transmitting system, numerical system and some key techniques are then introduced. The machine tool can be reconfigured when machining of arc worms and spatial cams beside of machining spherical hob. Four forms of the machine tool for machining different workpiece are also introduced.

Profile Error Synthetic Prediction Model for One-Side Milling of Spatial Cams

Based on the detailed analysis of the one-side milling theory of the spatial cam, an error comprehensive prediction model of the contour normal deviation is proposed in this paper by applying the spatial meshing theory, the rotation transformation of tensor and Newton’s iteration. A computer simulation example is presented, and the results show the error prediction model can disclosure and predict the law of influence effectively, that the tool and installation inaccuracy produce the contour normal error during the one-side processing of the spatial cam. Consequently, a scientific proof has been supplied to improve the precision and quality of the one-side milling of the globoidal indexing cam.

Formulating the swept envelope of rotary cutter undergoing general spatial motion for multi-axis NC machining

Based on the tangency condition in envelope theory and the body velocity representation in spatial kinematics, a closed-form solution of the swept envelope of a general rotary cutter moving along a general tool path defined in the NC programs is derived. No additional moving frames or local frames are required, and the computational formulas are independent of the types of the machines. The results can be applied to NC machining simulation, tool path optimization, and CAD/CAM of spatial cams.

An integrated tool for design, shape modelling and performance analysis of 3D cam

In this paper, an easy procedure to integrate three dimensional cam profile synthesis and Computer Aided Design is presented. The aim of the proposed method is to combine an accurate kinematic analysis with shape modelling using CAD programmes. In many cases, the manufacturing process and cutting approximation cannot be neglected and affect the final drawing. For specific needs, as spatial cams, an appropriate and more accurate synthesis is required. On the other hand, the only geometrical design misses all the advantages of modelling, for example the correct calculation of mass properties, interferences, and the possibility to perform dynamical and stress analysis. The authors develop an integrated tool which interacts with both CAD software and algebraic solver in order to draw an accurate cam model and to compute performances as regards errors on position, acceleration, jerk and jounce. This methodology can help the designers in the definition of digital mock-up.

Dimension Inspection of Spatial Cams by CNC Coordinate Measuring Machines

The problem of spatial cam inspection is still predominantly approached from simple gauging by manufacturers in today’s industry, despite the fact that Coordinate Measuring Machines (CMM) is both available and one of the most reliable and accurate metrological tools. Therefore, a kinematic model is presented in this paper to aid in the determination of the required NC data equations in order to move the probe to the desired position to inspect spatial cams on CNC CMM. This study originated from the need for advanced algorithms for the profile inspection of high precision manufactured spatial cams. To achieve this, the 4×4 homogeneous transformation matrix is employed to determine spatial cam profiles. Then, the CMM’s ability function matrix and the measuring-probe location matrix are derived. The desired NC data equations are obtained by solving the CMM link variables by equating the ability function matrix with the probe location matrix. A technique to minimize the sum of squared errors is also addressed by searching a best fit coordinate frame. To verify the validity of the method, this approach was implemented in software which was then used in a CNC CMM to measure a known spatial cam, with excellent results. The methodology developed in this paper can make the cam inspection process more flexible, automatic, and controllable. [S1087-1357(00)71001-X]

Profile Determination of Planar and Spatial Cams with Cylindrical Roller-Followers

A simple and useful procedure that can be used to determine profile surfaces of planar and spatial cams with cylindrical roller-followers is presented. Based on the rigid-body transformation between the cam and the roller-follower, the pitch (curve) surface which is the path of the point of the roller centre can be easily generated. Then the analytical profile surface of the cam can be represented by the offset surface of the pitch surface with a distance equal to the radius of the roller. To illustrate the ease and effectiveness of the approach, analytical expressions of profile surfaces of a disc cam, two cylindrical cams and two globoidal cams are typically given. Furthermore, in order to show the validity of this method, the results are then compared to those derived by an earlier procedure based on the screw theory.

Machining and dimensional inspection of spatial cams on 5-axis machine tools

An analytical methodology is developed for NC data generation to produce and measure spatial cams on 5-axis machine tools. The Denavit-Hartenberg notation is used for expressing the ability function of the employed machine tool and in the generation of the desired cutter/measuring-probe location. NC data equations are determined by equating the corresponding elements of the machine tool's ability function to the desired tool location matrices. To validate this methodology, a designed cam was machined and its surfaces were measured by an online measurement system equipped with a touch-trigger probe on a 5-axis machine tool. The resultant cutting speed and material-removal rate during machining are also investigated. This methodology is a general one and is applicable to various spatial cams. It also combines the activities of design, manufacturing, and measurement, thus making the production process more flexible, automatic, and controllable.

The machining and on-line measurement of spatial cams on four-axis machine tools

An analytical methodology has been developed for NC data generation in order to machine and measure a spatial cam on a four-axis machine tool. The Denavit-Hartenberg notation is used for characterizing the ability of the employed machine tool and in the generation of the desired tool location. NC data equations are obtained by equating the corresponding elements of the ability function of the machine tool and the desired tool location matrices. This methodology is a general one and is applicable to various spatial cams. It also combines the activities of design, manufacturing, and quality control, thus making the production process more flexible, automatic, and controllable.

The Application of Envelope Theory to the Surface Geometry of Spool Winding Cams

An approach to the analysis of the surface form of spatial cams, based on envelope theory, is illustrated. The method, previously developed by the authors, is applied here to spool winding cams. These groove-type barrel cams employ followers having flank radii significantly larger than the groove width, implying particular problems in defining the form of the cam surface. The capability presented here to precisely define the surface form is the necessary precursor for optimum design and manufacture.

A CAD/CAM system for spatial cams

Design and manufacture of cams are complicated engineering tasks which require usually lots of time and effort. Therefore, a CAD/CAM system for cams would be very useful. Recently, there has been an increasing demand from industry for automatic machines operating with spatial cams. This paper deals with a methodology of computer-aided design and manufacture of spatial cams. The computerized procedure is described in detail with accompanying examples

Synthesis of geared planar 4-bar linkages and cams to generate functions of two variables

Synthesis of almost all the mechanisms considered so far in the literature for two-degree-of-freedom function-generators result in highly nonlinear displacement equations necessitating special mathematical methods for their solution. A simple mechanism which combines an epicyclic gear train with a 4-bar linkage is proposed here. This device is based on simple theory and can develop a function of two independent variables very close to the desired function when iterative methods of solution are employed. Plate cams can also be combined with the gear train to generate functions of two variables. In fact this method enables the spatial cams to be replaced by plate cams. Example problems are included.