Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include, in at least one aspect, a fully automatic method of converting a generative design into an editable, watertight B-Rep by leveraging the generative solver input and representation to: (1) embed the exact input solid boundary surfaces where the design coincides with the input, (2) approximate everywhere else the design boundary with globally smooth, editable “organic” surfaces, and (3) join all surfaces to form a generative design output B-Rep.

Abstract: In a method for operating an at least two-axle machine tool, a geometric description of a path is specified, and according to the path, an advancing movement is carried out by simultaneously moving at least in one section a first axle and a second axle. A first maximum value for a first kinematic parameter relating to the advancing movement along the section of the path is defined by a control unit based on the geometric description. The advancing movement along the section is planned by the control unit by taking the first maximum value into consideration, and the axles are actuated so as to carry out the advancing movement according to the planned movement.

Abstract: In a method for manufacturing a three-dimensional shaped object, when an amount of a shaping material discharged toward a shaping surface per unit movement amount of a discharging unit is defined as a discharged shaping amount, in a layer forming step of forming a layer on the shaping surface, in a case in which a second partial shaped object to be shaped is not adjacent to a first partial shaped object that is shaped previously and is shaped with a gap between the first partial shaped object and the second partial shaped object, the second partial shaped object is shaped by setting the discharged shaping amount to a first discharged shaping amount, and in a case in which the second partial shaped object is adjacent to the first partial shaped object, the second partial shaped object is shaped by setting the discharged shaping amount to a second discharged shaping amount that is greater than the first discharged shaping amount.

Abstract: A three-dimensional shaped object manufacturing method includes a first step of acquiring shape data corresponding to a three-dimensional shaped object, a second step of generating, using the shape data, first intermediate data including path information indicating a path along which a depositing unit moves while depositing a shaping material and depositing amount information indicating a depositing amount of the shaping material, a third step of generating second intermediate data by changing the first intermediate data to increase an amount of the shaping material deposited and specifying a gap region interposed between regions where the shaping material is deposited according to the second intermediate data, a fourth step of generating shaping data by changing the first intermediate data or the second intermediate data such that the shaping material is deposited in the specified gap region, and a fifth step of shaping the three-dimensional shaped object according to the shaping data.

Abstract: A three-dimensional shaped object manufacturing method for shaping a three-dimensional shaped object. The three-dimensional shaped object manufacturing method includes a first step of shaping a first partial shaped object corresponding to a first partial path and a second partial shaped object corresponding to a second partial path in accordance with shaping data including path data and discharge amount data; a second step of measuring a first gap indicating a gap between the first partial shaped object and the second partial shaped object; and a third step of executing an adjustment processing of adjusting, based on a difference between the first gap and a second gap determined based on the shaping data and corresponding to the first gap, a discharge amount in a third partial path which is one of the plurality of paths and along which the discharge unit moves after the first partial path and the second partial path.

Abstract: A command-value generation apparatus includes: a segmentation unit to segment a machining program into execution units to generate segment machining programs; a parallel computation unit, including a plurality of arithmetic units, to execute the segment machining programs on a per execution unit basis in parallel and generate a segment command for each of the execution units, the segment command being a group of interpolation points on the tool path; and a command-value generation unit to generate a tool travel command from the segment command for each of the execution units. The segment machining programs are separate from one another by at least one segmentation point. The segment machining programs includes a forward segment machining program located forward of the segmentation point, and a rearward segment machining program located rearward of the segmentation point.

Abstract: The present invention sets a single machining point on a plurality of tool path rows, selects a machining point in a prescribed range with the point to be machined as the center, calculates the tool orientation at the point to be machined by way of averaging the tool orientation of the selected machining point of interest, corrects data pertaining to the tool orientation of the point to be machined by way of the calculated average tool orientation, acquires the shape data of a workpiece to be machined and the shape data of a ball end mill to be used, performs an interference check for the workpiece and the ball end mill on the basis of the corrected tool orientation data, and generates a new tool path on the basis of data pertaining to the corrected tool orientation when no interference between the workpiece and the ball end mill occurs.

Abstract: One embodiment of the present invention can be characterized as a method for controlling a multi-axis machine tool that includes obtaining a preliminary rotary actuator command (wherein the rotary actuator command has frequency content exceeding a bandwidth of a rotary actuator), generating a processed rotary actuator command based, at least in part, on the preliminary rotary actuator command, the processed rotary actuator command having frequency content within a bandwidth of the rotary actuator and generating a first linear actuator command and a second linear actuator command based, at least in part, on the processed rotary actuator command. The processed rotary actuator command can be output to the rotary actuator, the first linear actuator command can be output to a first linear actuator and the second linear actuator command can be output to a second linear actuator.

Abstract: Methods for preparing a hybrid article include disposing an additive structure comprising a plurality of layers on a build surface of a part, the build surface being defined based on x, and y coordinates, and the additive structure being defined by a three dimensional model defined by a series of planes based on x, y and z coordinates that define a plurality of layers, one layer comprising an interface surface having a contour being defined by x, and y coordinates. When the build surface and the interface surface are both oriented in space according to corresponding x, y and z coordinates, a cladding system is directed to deposit each of the sequential layers of the additive structure according to toolpaths that correspond with each of the plurality of layers of the three dimensional model.

Abstract: A process for providing a manufacturing modality for a hybrid article includes defining a model for a build surface on a part in a three dimensional space, and defining a model for an additive structure, the model including an interface surface of the additive structure that corresponds with the build surface in the three dimensional space. The process further includes orienting the x, y and z coordinates of each of the build surface of the part and the interface surface of the model in relation to a three dimensional work space, aligning contours of each of the build surface and the interface surface relative to the work space, and directing a cladding system to define toolpaths for two or more cladding layers that are defined by vertical planar segments or slices of the additive structure model.

Abstract: A control device of a machine tool includes an oscillation command generation part which generates an oscillation command for at least one feed axis based on a rotation speed of a spindle and a position command of the at least one feed axis so that the oscillation command becomes a positive non-integral multiple of the rotation speed and a tool intermittently cuts a workpiece, an oscillation command correction part which corrects the oscillation command using the position of the feed axis, and an addition part which adds the oscillation command corrected by the oscillation command correction part to a position deviation between the position command and the detected position of the feed axis.

Abstract: An exemplary volumetric reconstruction system accesses captured color and depth data for a surface of an object in a real-world capture space. The captured color and depth data is captured by capture devices positioned with respect to the real-world capture space to have different vantage points of the surface of the object. Based on the captured color and depth data, the volumetric reconstruction system generates reconstructed color and depth data for a volumetric reconstruction of the surface of the object. The generating of the reconstructed color and depth data includes allocating voxel nodes for surface points on the object within a voxel data store, determining and storing a confidence field value for each voxel node that accounts for a distance factor and a noise-reduction factor, and determining the reconstructed color and depth data using a raytracing technique based on the stored confidence field values within the voxel data store.

Abstract: A candidate point selection processor selects, as candidate points, vertices on an outline. A search point selection processor selects, from the candidate points, a reference search point to be used to search for a point that serves as a cutting line endpoint. A reference line setting processor sets a reference line connecting a reference point with the search point. A candidate line setting processor sets candidate lines connecting the search point with the candidate points other than the search point. A candidate line selection processor selects, as a selected candidate line, the candidate line located only within a non-effective region. An angle calculation processor calculates an angle between the reference line and the selected candidate line. A cutting line setting processor sets a cutting line connecting the search point with the candidate point of the selected candidate line defining an angle with the reference line that is the smallest angle calculated.

Abstract: A positioning apparatus includes a cutting line setting processor to set a cutting line to extend in a predetermined direction from a first endpoint on an outline of a target object located on a top sheet and to be located within a non-effective region, a first determination processor to determine whether a first angle between the outline of the target object and the cutting line, with the first endpoint located at an intersection of the outline and the cutting line, is equal to or smaller than a predetermined determination angle that is an acute angle, and a shape change processor to, when the first angle is determined to be equal to or smaller than the determination angle by the first determination processor, change the shape of the cutting line such that the first angle is greater than the determination angle.

Abstract: A method for cutting a plow bolt hole in a work piece using a cutting torch includes receiving a computerized part file including elements representing holes to be cut in the work piece. An element is selected and assigned a plow bolt hole identity. The selected element is associated with an aspect of an inner shape and an aspect of an outer shape of the plow bolt hole. A tool path is developed for the cutting torch that accounts for the aspect of the inner shape and the aspect of the outer shape and is associated with the selected element. Instructions are output to a computer numerical control (CNC) machine to move the cutting torch along the tool path so as to cut both the inner shape and the outer shape of the plow bolt hole in the work piece consecutively without interrupting a flame of the torch.

Abstract: A numerical controller of the present invention is a numerical controller for controlling a machine having two or more paths based on a machining program for a single path in which two or more tools are moved in a radial direction of the workpiece and a direction parallel to the axis of rotation to perform cutting, and includes path assignment means for dividing the machining program into cutting motion groups by using rapid motions as delimiters, assigning the cutting motion groups which are divided to the two or more paths, and generating path assignment information in which the cutting motion groups which are assigned are overlapped between a cutting motion group located earlier on the machining program and a cutting motion group located later such that a cutting position by the cutting motion group located later does not overtake a cutting position by the cutting motion group located earlier.

Abstract: Presented are embodiments for the generation of point clouds on a surface. A surface is described by a mathematical function. The surface may be subdivided into a plurality of patches, a plurality of triangles, or a plurality of rectangles, inter alia. A plurality of points are calculated and distributed among the patches, triangles, or rectangles comprising the surface. Generation of such point clouds may be useful in rendering N-dimensional surfaces for display or output on computer display or output devices.

Abstract: The numerical controller detects an abnormal interference between targets for interference check in a machine tool, including a tool and a workpiece, based on a machining program. The numerical controller changes a direction (contactable direction) in which the tool can contact the workpiece for machining and determines that an interference between the tool and the workpiece is abnormal if the tool compensation direction of radius compensation is not included in the changed contactable direction for the tool.

Abstract: A numerical controller capable of automatically calculating a tool path based on a command of a cutting path in skiving machining includes a command analysis unit that determines whether a block read from a machining program corresponds to a skiving machining command, a skiving machining command data calculation unit that calculates a path and a feed speed of a tool based on a path of a cutting point and a feed speed of the cutting point commanded by the skiving machining command when the command analysis unit determines that the block corresponds to the skiving machining command, and an interpolation unit that calculates interpolation data according to a progress rate of the block during actual machining based on the path of the tool calculated by the skiving machining command data calculation unit and a coordinate value during actual machining.

Abstract: Systems and Methods for Computer Numerically Controlled (CNC) devices comprising a CNC integrated Computer-Aided Manufacturing (CAM) controller configured to input a CAD file and output a CAM file and a CAM integrated CNC controller configured to input the CAM file and output at least one command for at least one servo controller of a set of one or more servo controllers.

Abstract: Various systems, methods and devices for capturing digital images of an object in a region of interest and for identifying points on the surface of an object in a region of interest are disclosed. A device operable to capture digital images of an object in a region of interest includes a support structure having an object support surface at the bottom of the region of interest; a scan head incorporating an imaging system comprising at least one digital imaging device located with respect to the support structure to have a field of view that includes a segment of the region of interest; and a first motive system operable to move the scan head along a fixed path between first and second vertical positions with respect to the support structure thereby to cause the at least one digital imaging device to have a field of view that includes a different segment of the region of interest. Various related systems, methods and devices are disclosed.

Abstract: An operation of a processing machine with redundant actuators is controlled according to a reference trajectory by selecting, from a set of points forming a segment of the reference trajectory to be processed for a period of time, a subset of points corresponding to a fraction of the period of time. The subset of points is selected such that the redundant actuators are capable to position the worktool at each point in the subset within the period of time and are capable to maintain the worktool at the last point of the subset after the period of time while satisfying constraints on motion of the redundant actuators. The segment of the reference trajectory is modified in the time domain and the control inputs for controlling the motion of the redundant actuators are determined using the modified segment of the reference trajectory.

Abstract: When graphic information is selected, program creating unit receives machining shape data from graphic information analysis unit and pivot axis information from rotation center storage unit. Based on the received data, the program creating unit generates a new amount of movement of a wire electrode relative to a workpiece and the amounts of rotation of pivots, used to machine the workpiece with the wire electrode held vertical.

Abstract: A method for accurately assembling and positioning a modular tooling structure for manipulating a workpiece includes receiving, at one or more computers, three-dimensional model information describing the workpiece; generating, at the one or more computers, three dimensional design information representing a configuration for the modular tooling structure, wherein the three dimensional design information includes position data describing a position for at least one engaging member of the modular tooling structure with respect to the workpiece; positioning a multi-dimensional gauge with respect to a base structure based on the position data; and assembling the modular tooling structure using the design information such that a first end of the modular tooling structure is connected to the base structure and the at least one engagement member is positioned at a second end of the modular tooling structure and is in engagement with the multi-dimensional gauge.

Abstract: A method of controlling a machine tool and other controlled devices, as well as a programmable numerical control (PNC) system, are disclosed. In at least one embodiment, the method of controlling includes receiving a first part program at a programmable logic controller (PLC), and storing the first part program in a string array library of a memory portion of the PLC. The method further includes communicating information between the PLC and an operator interface regarding the first part program, and providing a first signal from the PLC to a first port so as to cause the first machine tool to be operated in accordance with the first part program. Also, in at least some embodiments, the PNC system allows for control of multiple machine tools and/or other controlled devices, by way of one or more part programs, and/or for editing of a part program while that program is being executed.

Abstract: Systems and Methods for Computer Numerically Controlled (CNC) devices comprising a CNC integrated Computer-Aided Manufacturing (CAM) controller configured to input a CAD file and output a CAM file and a CAM integrated CNC controller configured to input the CAM file and output at least one command for at least one servo controller of a set of one or more servo controllers.

Abstract: A numerical controller controls a multi-axis machining machine having three linear axes and three rotation axes that include one rotation axis for tool phase control. The numerical controller interpolates smoothly a tool center point position and a tool posture (tool direction and tool phase direction) on the basis of a tool center point position instruction and a tool posture instruction; works out an interpolated tool center point position and an interpolated tool posture (interpolated tool direction and interpolated tool phase direction), and, on the basis of the interpolated tool center point position and the interpolated tool posture that have been worked out, calculates each position of the three linear axes and three rotation axes of the multi-axis machining machine, such that the respective axes are driven to the calculated position.

Abstract: Embodiments of the present disclosure generally pertain to systems and methods for interfacing with a network access device (“NAD”). An NAD in accordance with an exemplary embodiment of the present disclosure comprises an interface extension extending from a housing of the NAD. The interface extension comprises a cable and an enclosure that is sealed by a removable cap. The cable extends from a port on the housing, and the enclosure is positioned on the cable a desired distance from the housing. The removable cap screws onto the enclosure to form a water-tight chamber within the enclosure. The interface extension further comprises an interface connector connected to an end of the cable, and the interface connector is positioned within the chamber when the removable cap is screwed onto the enclosure. When access to the NAD is desired, a technician removes (e.g. unscrews) the removable cap from the enclosure and connects the interface connector to a user interface device.

Abstract: Rough machining of a workpiece is performed by a numerically controlled machine tool using an adaptive toolpath technique. Material removal rate and machine efficiency are increased by forming a pre-roughing slot in the workpiece along medial axes, and machining the remainder of the workpiece using a toolpath that begins inside the pre-roughing slot and spirals outwardly in smooth curves.

Abstract: A set of costs representing operations of a machine along a set of trajectories connecting a set of exit and entry points on contours of a pattern is determined. Each trajectory represents an operation of the machine proceeding from an exit point with an exit velocity to an entry point with an entry velocity according to dynamics of the machine. The set of trajectories includes at least one trajectory representing the operation along a contour with non-zero velocities at corresponding exit and entry points, and at least one trajectory representing the operation between different contours with non-zero velocities at the corresponding exit and entry points. A sequence of the trajectories optimizing a total cost of operation of the machine tracking the pattern is determined based on the costs, and a set of instructions for controlling the machine is determined according to the sequence.

Abstract: Herein are provided methods, systems, computer-readable media, techniques and processes for surface manipulation in dental prosthesis design. These include providing an interface for modifying the surface of a model of a dental prosthesis. This interface may be provided to an operator, dentist, dental practitioner, or any other appropriate person via a computer and a computer display. The operator provides areas in which the operator would like to add a layer or other limited manipulation to the surface of the model. This may include an addition to the surface or a subtraction from the surface. As the operator is defining additional areas to manipulate on the surface (e.g., add or subtract a layer), invariably some of them will overlap. Unlike previous methods, this overlap will not cause the amount added to the surface to increase beyond the predefined limit for the layer. This allows operators to define cleanly added layers or cleanly subtracted layers from dental prostheses.

Abstract: In a moulder, at least one rotatably driven tool (7, 8, 10, 11) is used to produce the structure (27) or contour on the workpiece (1) by workpiece removal. The workpiece positions along the workpiece (1) for producing the structure or contour are set depending on the data of the workpiece (1) and of the tool (7, 8, 10, 11). The data are transmitted to the machine controller which processes the CNC program based on the data during the passage of the workpiece (1) through the moulder and moves the tool (7, 8, 10, 11) into the required positions via CNC drives depending on the workpiece position. The workpiece position is sensed during the passage of the workpiece (1) through the moulder. In order to sense the workpiece position in the moulder, at least one measuring element (18) is provided upstream and downstream of the tool (1), said measuring element (18) being connected to the machine controller and supplying signals that describe the advancing travel of the workpiece (1) to the machine controller.

Abstract: A computing device compensates a coordinate of a position device for a computerized numerical control (CNC) machine. The computing device generates a point cloud according to contour points of the position device. The computing device deletes selected contour points from the point cloud upon the condition that the distance corresponding to each selected contour point exceeds a predetermined threshold. The computing device calculates an average coordinate of the contour points which are remained in the point cloud.

Abstract: A machining curve creating apparatus create curve of a tool used to machine a workpiece by repeating a procedure of taking, as a partial point sequence, a part of a point sequence expressing the tool path and generating a partial curve. The machining curve creating apparatus includes stored-information-utilized curve generating unit for generating a partial curve utilizing segmented curve information. When curve information utilization determining unit determines to utilize the stored information, the stored-information-utilized curve generating unit generates a partial curve.

Abstract: A system and method for positioning a fluid stream for cutting a double contour workpiece includes a compensation module configured to receive information regarding a contour path in at least five degrees of freedom for cutting the double contour workpiece and a velocity of movement of the fluid stream during cutting and configured to provide as an output a modified contour path of said at least five degrees of freedom based on Kerf compensation errors. A motion controller is adapted to receive the modified contour path of said at least five degrees of freedom and the velocity and is configured to provide control signals. A positioner is configured to receive the control signals and position a fluid stream adjacent the workpiece accordingly.

Abstract: Methods and devices for milling a channel-shaped cavity by a five-axis computer numerical control (CNC) machine by selecting a workpiece to be machined, determining cutting tool flow along the channel-shaped cavity, determining cutting tool in-depth penetration, determining a trochoid path, and determining auxiliary movements.

Abstract: An optimum cutting feed rate of a machine tool is calculated at the outset and a tool path as well as the optimum cutting feed rate calculated is directly output to a driving unit of the machine tool. A relative movement between the work and a tool is made to occur along the tool path at the optimum cutting feed rate for each part of the tool path. To this end, a control system includes a CL data generating unit 32, a CL data memory 33, a driving capability data memory 34, a cutting feed rate data generation unit 35, a cutting feed rate data memory 36, and a controller 42.

Abstract: This invention provides a novel tool path planning method for five-axis flank milling by imposing the constraints of curve interpolation on the tool path. The tool motion is described in the form of spline curves during its optimization-driven calculation process, instead of discrete cutter locations in CNC linear interpolation. The coefficients of the curve equations are generated by minimizing accumulated geometrical errors on the machined surface using optimization algorithms. The continuity imposed by the spline motion reduces uneven modifications of cutter locations during the optimization process. The resultant tool path yields superior.

Abstract: A system and method of generating machine marking instructions for marking an ophthalmic lens is disclosed. The method comprises the steps of receiving lens order data related to a lens order, receiving an initial marking layout and calculating, using the lens order data, ophthalmic lens data of an ophthalmic lens related to the lens order. The method also comprises the steps of determining, using the ophthalmic lens data, marking parameters relating to the ophthalmic lens, producing an additional marking layout by modifying the initial marking layout using the marking parameters and the lens order data, the additional marking layout representing the markings to be applied to the ophthahmc lens, and generating machine marking instructions arranged to cause a marking machine to mark the ophthalmic lens in accordance with the additional marking layout.

Abstract: Vibration protection in a compressor system with a variable speed compressor may include operating a variable speed compressor of a compressor system at a first frequency, measuring a vibration of the compressor system at the first frequency, determining whether the vibration exceeds a maximum vibration value, and operating the variable speed compressor at an average frequency equivalent to the first frequency, when the vibration exceeds the maximum vibration value, by identifying an allowed upper frequency and an allowed lower frequency, calculating an upper operating time and a lower operating time, and operating the variable speed compressor at the allowed upper frequency for the upper operating time and the allowed lower frequency for the lower operating time.

Abstract: A work having a non-circular cross-section is machined by relative movement between the work and a tool, as the relative position and angle between the work and tool are changed at least within a plane including the cross-section of the work. In machining along a preset tool path, the difference between the relative angle at a point on the preset tool path which machining is started and that point on the preset tool path at which machining is finished is calculated. Time needed in machining along the preset tool path is equally divided by a preset number at equal time divisions, and positions on the tool path corresponding to equal time divisions are set as tool path points. When the tool moves through each point, the relative angle is continuously changed an angle corresponding to division of the difference of the relative angles by the preset number of equal time divisions.

Abstract: A CPU 41 reads a next block (S1), and then determines whether the read block is a TCP (tool center point) control finish command “G49” or not (S2). If it is determined to be the TCP control finish command “G49”, the TCP control is finished. If it is determined not to be the TCP control finish command “G49”, whether the read block is a coordinate-system transformation command “P1” or not is determined (S3). Next, if it is determined not to be the coordinate-system transformation command “P1”, the TCP control is performed, without transforming the coordinate system, in accordance with a command of the block (S11). Next, the process returns to S1, and then the process after S1 is executed.

Abstract: A motion command is constructed based on an optimized acceleration pulse designed to control the spectral content of the commanded acceleration. By way of judicious design of the pulse shape, the majority of the energy in the command is contained in a narrow baseband and rolls off rapidly in frequencies outside that band. Additionally, the command can be constructed to suppress selected frequency content in one or more attenuation bands outside the baseband. The resulting motion command permits rapid motion control, while avoiding the excitation of unwanted resonant response in the system while remaining tolerant of system uncertainty.

Abstract: A system and method for machining a work-piece in restrictive access operating position is disclosed. The system includes a robot arm adapted to access the bottom face of the work-piece; a computation means adapted to compute a central line on the bottom face while ascertaining an area of overlap that is accessible from all sides of the work-piece; and a robot controller adapted to sequentially maneuver the robot arm from one side of the work-piece to other side of the work-piece on the bottom face. Other embodiments are also disclosed.

Abstract: A method for monitoring a production process with regard to quality is disclosed. The method includes: a) breaking down the production process into a sequence of individual steps, defined by a sequence of control commands for a production program for carrying out the production process on a machine tool; b) generating at least one signal template per individual step of the production process from the control commands for the individual steps, each signal template corresponding to a theoretical signal curve for a parameter which may be measured upon executing the production process; c) measurement of a signal curve for at least one parameter per individual step during the execution; and d) comparison of the or each measured signal curve with the respective arithmetically generated signal template, wherein a qualitatively poor production process is determined if the measured signal curve deviates from the signal template by more than a given tolerance.

Abstract: A system, method, machine-readable medium for accurate simulation of automated machinery. A method includes loading a machine operating model. The method also includes receiving machine-specific data from an automated machinery controller. The method also includes simulating a machine operation using the machine-specific data and the machine operating model to produce optimized motion data. The method includes transmitting the optimized data to the automated machinery controller by the simulation data processing system.

Abstract: A numerical controller configured to control a machine tool for machining the workpiece on the basis of a machining program composed of a plurality of blocks includes a corner multiple curves inserting unit. This corner multiple curves inserting unit inserts, between consecutive two blocks, three cubic polynomial curves in which a position, a direction and a curvature are continuous and the distances from these two blocks are within a prescribed allowable tolerance, if a direction or a curvature between these two blocks is discontinuous in the machining program.

Abstract: Rough machining of a workpiece is performed by a numerically controlled machine tool using an adaptive toolpath technique. Material removal rate and machine efficiency are increased by forming a pre-roughing slot in the workpiece along medial axes, and machining the remainder of the workpiece using a toolpath that begins inside the pre-roughing slot and spirals outwardly in smooth curves.

Abstract: A set of costs representing operations of a machine along a set of trajectories connecting a set of exit and entry points on contours of a pattern is determined. Each trajectory represents an operation of the machine proceeding from an exit point with an exit velocity to an entry point with an entry velocity according to dynamics of the machine. The set of trajectories includes at least one trajectory representing the operation along a contour with non-zero velocities at corresponding exit and entry points, and at least one trajectory representing the operation between different contours with non-zero velocities at the corresponding exit and entry points. A sequence of the trajectories optimizing a total cost of operation of the machine tracking the pattern is determined based on the costs, and a set of instructions for controlling the machine is determined according to the sequence.

Abstract: An automated computer-implemented method for generating commands for controlling a computer numerically controlled milling machine to fabricate a machined object from a workpiece, the machined object being configured to facilitate subsequent finishing into a finished object, the method including defining a surface of the finished object, defining an offset surface defining an inner limiting surface of the machined object, defining a scallop surface defining an outer limiting surface of the machined object and calculating a tool path for the milling machine which produces multiple step-up cuts in the workpiece resulting in the machined object, wherein surfaces of the machined object all lie between the inner limiting surface and the outer limiting surface and the number of step-up cuts in the workpiece and the areas cut in each of the step-up cuts are selected to generally minimize the amount of workpiece material that is removed from the workpiece.