Abstract: Provided are an apparatus and method of aligning optical axes of lenses and assembling a camera module that are capable of adjusting the optical axes of the lenses. The apparatus for aligning the optical axes of the lenses and assembling the camera module includes a support block to support a substrate at which an image sensor is installed, a displacement sensor to measure a tilted state of the image sensor, a fastener to fasten or loosen fastening components to couple a lens holder to the substrate, and a controller to control a fastening level of the lens holder by the fastener to correct a tilted state according to a measurement result of the displacement sensor. The optical axis of the lens can be rapidly and precisely adjusted and assembled by use of the above described apparatus and method.

Abstract: A C-type CNC machine center generally includes a chassis, a displaceable table, a work table, a working spindle, a coupling seat, and a driver device. The chassis has a working area, a power area, and a displacement channel communicating with the working area and the power area. The displaceable table is slidably mounted to the chassis and located in the working area. The coupling seat is slidably coupled to the base seat in the power area and includes an elongate hollow body and is fixedly mounted, with an end thereof, to the displaceable table. The driver device includes a motor mounted to the base seat in the power area and a ball screw coupled to the motor and the coupling seat to drive the coupling seat and the displaceable table to synchronously conduct reciprocal movement in a given direction. The coupling seat separates the ball screw from the working area.

Abstract: A precision pneumatic drill spindle and method provides reduced spin axis error and increased rate of forming holes in a microelectronic substrate. The spindle includes a press-fit collar that accepts drill bits and incorporates turbine blades around the collar, which is rotated by directing pressurized air through a number of nozzles distributed around the collar within a housing of the spindle. The collar is supported by air bearings above and below the collar. The turbine blades may be provided by concavities in the collar forming a Pelton wheel type rotation system that concentrates the air flow to improve energy transfer from the pressurized air directed by the nozzles to the collar, increasing the rotation rate of the collar. Exit air may be directed downward toward the tip of the drill bit by inclined channels within the lower air bushing assembly, improving the debris removal rate.

Abstract: A workpiece conveying apparatus for a pressing machine includes: a first arm supported so as to be rotatable within a substantially horizontal plane; a second arm supported on the first arm so as to be rotatable within the substantially horizontal plane; a workpiece holding device supported on a distal end side of the second arm so as to be rotatable within the substantially horizontal plane; a first arm drive mechanism configured to drive the first arm to rotate; a second arm drive mechanism configured to drive the second arm to rotate with respect to the first arm; a workpiece holding device rotation drive mechanism configured to drive the workpiece holding device to rotate with respect to the second arm; and a tilt drive mechanism configured to drive the workpiece holding device to rotate with respect to the second arm.

Abstract: A handheld work apparatus has an electric motor and a voltage source for operating the motor. A manual actuation element provided on a handle of the apparatus is operated by a user and is provided for activating the motor. The actuation element is connected to a control unit which controls the energy supply from the source to the motor as a function of an operating signal of the actuation element. If the control unit is in a blocking state, the energy supply to the motor is blocked independently of the operating signal of the actuation element. After receiving a control signal, the control unit switches from the blocking state to a standby state to release an energy supply to the motor. The control signal is derived from a combination of an actuation stroke and an actuation time (?TB) of the actuation element. A method for activating the apparatus is also disclosed.

Abstract: A workpiece machining system including a setting-up module and a machining module for producing workpieces. The setting-up module includes at least one first tool-holder attachment device for removably attaching at least one tool-holder and at least one first workpiece-carrier attachment device for removably attaching a workpiece-carrier. The machining module includes at least one second tool-holder attachment device for removably attaching at least one tool-holder and at least one second workpiece-carrier attachment device—for removably attaching a workpiece-carrier, such that the tool-holder and the workpiece-carrier—can both be transferred after setting up from the setting-up module to the machining module.

Abstract: A control device for a piece of powered equipment having an electronic sensor and an electronic control board for controlling the equipment depending on a control signal from the sensor. The electronic sensor is a contactless optical sensor, provided in an interface area of the control device, configured to measure a distance separating at least one target, located in the interface area, and the optical sensor, the electronic board being configured to establish a first control of a main function of the powered equipment, when a signal from the optical sensor is established for a measured distance within a first range of distances, and to establish a control for at least one additional function of the powered equipment, different from the main function, when a signal from the optical sensor is established for a measured distance greater than the first range of distances.

Abstract: A tool shape measurement apparatus for imaging a tool is provided with: a camera for imaging the tool disposed at a previously determined imaging position; a shutter disposed on the opposite side of the tool from the camera; an illuminating device for shining light toward the shutter; and a control device for calculating the shape of the tool from an image of the tool. The illuminating device is disposed so that an image in which the tool is darker than the background of the tool is captured due to light reflected at the reflecting surface of the shutter.

Abstract: A method of providing an easy-clean, water-sheeting coating on a substrate includes: abrading a surface of a substrate using an abrasive article to provide an abraded surface having a surface roughness R?a#191 in a range of from 100 nm to 3500 nm, contacting a coatable composition with the abraded surface, and removing water from the coatable composition. The coatable composition comprises silica nanoparticles and has a pH of 7.5 or less. A kit including the abrasive article and the coatable composition is also disclosed.

Abstract: A steady rest for supporting, e.g., bearing points on shaft parts of crankshafts, during the grinding of central and/or eccentric workpiece regions. For the grinding, the steady rest is brought from a retracted position to a supporting position against the workpiece region to support the workpiece region at respective circumferential regions. The supporting parts are each arranged on a lateral flank of a prism opening in a fork-like manner on a steady-rest arm in a fixed position in relation to each other and to the steady-rest arm, the supporting parts thus forming an opening angle to each other. The supporting parts are arranged below center with respect to the longitudinal axis of the workpiece region such that an angle bisector between the two supporting parts has a fixed acute angle to the vertical extending through the longitudinal axis of the workpiece region and the CNC-controlled advancement occurs along said angle bisector.

Abstract: There is provided a circumference calculating device including an expected shape specifying part 201b configured to obtain an expected finish shape of a bevel in consideration of an interference amount of a beveling tool when beveling is performed to an uncut spectacle lens; and a theoretical circumference calculating part 201d configured to obtain a bevel circumference of the spectacle lens having the expected finish shape obtained by the expected shape specifying part 201b, as a theoretical circumference of this spectacle lens.

Abstract: An inner cam has a substantially C-shaped cross section, an arcuately shaped inner circumferential surface of which is ground with high precision by such a honing method. The inner circumferential surface has a discontinuous portion. The honing method includes a fixing step and a grinding step. A plurality of inner cams, in which openings are provided between both ends thereof in the circumferential direction, are stacked, and the arcuately shaped inner circumferential surfaces thereof are subjected to grinding. In the fixing step, the relative positions of the plurality of inner cams are fixed such that a resultant force against the inner cams arranged on both end sides in the stacking direction, and a resultant force against the inner cams arranged on a central side in the stacking direction are opposed to each other mutually at a center location of the stacking direction.

Abstract: The present disclosure relates to a grinding method for grinding of non-circular workpieces with an improved productivity and quality of the resulting workpiece. The method comprises a first and a second stage. The rotational speed profile of the workpiece in the first stage is controlled with the purpose of maintaining a pre-selected maximum surface temperature of the workpiece during said first stage, and grinding of the workpiece in said second stage is performed while controlling an aggressiveness number of said second stage so as to achieve an intended final surface quality. The present disclosure also relates to a method for determining the processing parameters of such a grinding method wherein the first and the second stage of the grinding method are iterated to thereby determine the processing parameters leading to a high productivity and desired quality of the workpiece after grinding.

Abstract: In one embodiment, a polishing head includes an elastic film configured to form pressure rooms to which a pressure fluid is fed, and configured to press a substrate onto a polishing surface with a fluid pressure of the pressure fluid. The head further includes a first magnetic generator provided above a partition wall that separates the pressure rooms. The head further includes a second magnetic generator configured to form at least a portion of the partition wall or provided below the partition wall.

Abstract: A polishing apparatus has a polishing pad, a top ring for holding a semiconductor wafer, and a vertical movement mechanism operable to move the top ring in a vertical direction. The polishing apparatus also has a distance measuring sensor operable to detect a position of the top ring when a lower surface of the top ring is brought into contact with the polishing pad, and a controller operable to calculate an optimal position of the top ring to polish the semiconductor wafer based on the position detected by the distance measuring sensor. The vertical movement mechanism includes a ball screw mechanism operable to move the top ring to the optimal position.

Abstract: The present invention provides a chemical mechanical (CMP) polishing pad for polishing, for example, a semiconductor substrate, having one or more endpoint detection windows (windows) which at a thickness of 2 mm would have a UV cut-off at a wavelength of 325 nm or lower which are the product of a reaction mixture of (A) from 30 to 56 wt. % of one or more cycloaliphatic diisocyanates or polyisocyanates with (B) from 43 to 69.9999 a polyol mixture of (i) a polymeric diol having an average molecular weight of from 500 to 1,500, such as a polycarbonate diol for hard windows and a polyether polyol for soft windows and (ii) a triol having an average to molecular weight of from 120 to 320 in a weight ratio of (B)(i) polymeric diol to (B)(ii) triol ranging from 1.6:1 to 5.2:1, and a catalyst, preferably a secondary or tertiary amine or bismuth neodecanoate, all weight percent's based on the total solids weight of the reaction mixture.

Abstract: A polishing solution includes a fluid component and a plurality of ceramic abrasive composites. The ceramic abrasive composites include individual abrasive particles uniformly dispersed throughout a porous ceramic matrix. At least a portion of the porous ceramic matrix includes glassy ceramic material. The ceramic abrasive composites are dispersed in the fluid component.

Abstract: Polishing pads having a polishing surface with continuous protrusions are described. Methods of fabricating polishing pads having a polishing surface with continuous protrusions are also described.

Abstract: A method of producing a polishing head including: a backing pad, for holding a workpiece back surface, stuck on a lower portion of a rigid body; and a ring template, for holding a workpiece edge, disposed on a lower surface of the backing pad. This polishing head brings a front surface of the workpiece into sliding contact with a polishing pad attached on a turn table while holding the workpiece back surface on the lower surface of the backing pad. The method includes sticking the backing pad on the lower portion of the rigid body with a double-sided tape under a reduced pressure without heating; and sticking the template on the backing pad with a double-sided tape or a liquid or paste reaction curable adhesive containing no solvent under a reduced pressure without heating. This method can polish the workpiece into a very flat workpiece.

Abstract: A method for manufacturing a face seal may generally include positioning a machining device relative to the face seal such that the face seal is compressed between a machining surface of the machining device and a support member on which the face seal is supported. In addition, the method may include removing material from a seal flange of the face seal using the machining device while the face seal remains compressed between the machining device and the support member and monitoring a compressive load applied through the face seal as material is being removed from the seal flange. Moreover, the method may include adjusting the operation of the machining device to prevent further removal of material from the seal flange when the monitored compressive load is equal to a predetermined load setting.

Abstract: A planarization device includes a planarization pad and a pad conditioner over the planarization pad. The pad conditioner includes a rotatable plate having a lower surface separated from an upper surface of the planarization pad by a predetermined distance and at least one nozzle opening on the lower surface of the rotatable plate.

Abstract: A CMP pad conditioner for conditioning a polishing pad. Various embodiments of the disclosure include a plurality of elongated protrusions which work a conditioned surface of a polishing pad at a variety of attack angles as the CMP pad conditioner engages the polishing pad. Because of the elongated geometry of the protrusions, the variety of attack angles will tend to flex the conditioned face of the polishing pad in a multifaceted manner. Such multifaceted manipulation of the conditioned face enhances the cut rate of the conditioner assembly and the removal of debris in the pores of the polishing pad that are residual from the CMP process, to better open the pores of the polishing pad and to better maintain the removal rate in the CMP process.

Abstract: An abrading device includes a funnel and an outlet orifice disposed within the funnel for passage of abrasive material, where a distance between the outlet orifice and a bottom end of the funnel is adjustable. An exhaust tube is coupled to the funnel for withdrawal of spent abrasive material from the funnel.

Abstract: Apparatuses and systems that enable selective removal of protective coatings from substrates are disclosed. Such a material removal system may use pressurized solid carbon dioxide (CO2) (i.e., dry ice) to remove a selected portion of a protective coating from a substrate. The material removal system may include one or more templates that provide selectivity in removing protective coatings from one or more substrates, fixtures for holding one or more substrates in place while material removal processes occur and apparatuses for positioning one or more substrates at desired locations in material removal systems.

Abstract: Structured abrasive articles include a backing and shaped abrasive composites secured to the backing. The shaped abrasive composites include abrasive grits dispersed in a binder matrix. The shaped abrasive composites include a bottom surface and a top surface opposite and not contacting the bottom surface, and at least three sidewalls abutting both the bottom and top surfaces and two other sidewalls. In one embodiment, at least two cusps are formed by the top surface and individual sidewalls. In another embodiment, the top surface includes at least two triangular facets that contact at least two respective sidewalls and at least two cusps. The top surface includes at least one interior recessed portion nearer the cusps than the bottom surface. Methods of abrading a workpiece using the structured abrasive article are also disclosed.

Abstract: Embodiments of the invention relate to methods of making articles having portions of polycrystalline diamond bonded to a surface of a substrate and polycrystalline diamond compacts made using the same. In an embodiment, a molding technique is disclosed for forming cutting tools comprising polycrystalline diamond portions bonded to the outer surface of a substrate.

Abstract: Apparatuses and methods of operating the same are described. An apparatus may include a substrate that is formed of substantially flexible material. The substrate may include a first portion, a second portion, and a fold line. The first portion may include an inner surface with an adhesive material. The second portion may include an inner surface with an adhesive material. The fold line between the first portion and the second portion which enables the substrate to be folded. The fold line may extend from a location at an edge of the substrate. A bottom part of the inner surface of the first portion and the second portion may adhere to a front and back surface of a card and a middle part of the inner surface of the first portion and the second portion may adhere to an edge of the card.

Abstract: A method for operating a power tool for screwing a screw into a workpiece. After an activation of the power tool, an electric motor is driven in order to screw the screw into the workpiece. The rotation speed of the electric motor while the screw is being screwed in is ascertained during a predefined initial time of an impact operating mode of the power tool. A rotation speed of the electric motor is ascertained after the initial time. A torque of the electric motor is at least reduced if the ascertained rotation speed of the electric motor exceeds a predefined rotation speed limit.

Abstract: A pressurized fluid container for use with a fastener-driving tool, the container having an outer shell defining an inner chamber, having an open neck and an effective height, a closure sealingly engaged on the open neck, and a tube depending from the closure.

Abstract: The disclosure describes an adapter for a multifunctional electric drill which has a first bearing and a second bearing both disposed in an outer housing. By means of a transmission shaft disposed in the outer housing by using the first bearing and the second bearing, a swinging bearing mounted on the transmission shaft and a sliding rod connected to the swinging bearing, a preset angle is formed between the axis of the swinging bearing and the axis of the transmission shaft. A transmission shaft is fixed by using double bearings, rotation is stable, noise is low, and the service life is long; the rotation movement is converted into the straight reciprocating movement of a sliding rod by means of an inclined swinging bearing, and the energy conversion rate is high.

Abstract: A power tool includes a housing, an output shaft, and a tool holder connected to the output shaft. A rotor assembly is attached to the output shaft that is configured to be acted on by a fluid flow through the housing to cause rotation of the output shaft. A centrifugally movable fluid flow governor is coupled to the output shaft that is configured to move outwardly from the output shaft to alter a force acting on the rotor assembly when the output shaft reaches a predetermined speed.

Abstract: A portable working machine including: a driving source; a main body including the driving source; a handle joined with the main body; a fixing portion provided to one of the main body or the handle; and a vibration-proofing mechanism including an elastic body, the handle joined with the main body with the vibration-proofing mechanism and the fixing portion interposed therebetween; wherein the elastic body of the vibration-proofing mechanism is fixed to a first side of the fixing portion, and a stopper portion configured to come into contact with the other of the main body or the handle to regulate a movement amount of the handle is provided at a second side of the fixing portion, which is opposite to the first side of the fixing portion.

Abstract: A rail has a guide surface on which the locking block is guided in a bearing manner between a position locking the bar, in which the toothed side engages in the toothed long side, and an unlocked position, in which the toothed side is not engaged with the toothed long side. A spring pretensions the locking block into the locking position. The guided side and/or the guide surface have a flank that is inclined with respect to the bar axis such that the locking block is forced in the direction of the bar in the event of a movement along the bar axis.

Abstract: Systems, method and apparatus for a fixturing platform having a frame assembly configured to couple to a support assembly with a plurality of surface plates configured to couple to the frame assembly in a number of configurations are described in this disclosure. The configurations include a continuous configuration with abutting surface plates forming a continuous working surface and a spaced configuration with spaced surface plates forming a spaced working surface, the spaced configuration have one or more working gaps between surface plates.

Abstract: A stack arrangement having at least two stack elements, which can be stacked on each other in a stacking direction, of which at least one is formed from a transport container which has a container body having a storage receptacle which has a machine receptacle for an electrical or pneumatic hand tool machine. The stacking elements have bus interfaces for transferring data and/or energy between the stacking elements of the stack arrangement, wherein the bus interfaces form a bus connection between the stack elements when the stack elements are stacked on each other.

Abstract: Storage equipment including at least one storage container with a vertical axis, on which a coupling bar, which can rotate about a rotational axis that is at a right angle to the vertical axis, is mounted on the outside, in the upper region of the front side of same. The coupling bar is designed as a pivot bar with only one arm, which is provided with an individual bar arm, projecting away from the rotational axis on one side, on which a coupling structure is arranged. The pivot angle of the pivot bar is limited to 90° by a stop, and the pivot bar can be pivoted exclusively between an inactive standby position with the bar arm oriented at a right angle to the vertical axis, and an active coupling position projecting upwards in the axial direction of the vertical axis.

Abstract: A storage hutch assembly 10 including a plurality of dissimilar storage assemblies, such as power tool holder assembly 120, which may be selectively and operatively deployed within the hutch assembly 10 upon a contained shelf 30 and/or upon a storage cart, such as cart 50, and/or upon a surface such as surface 25 contained within the storage hutch assembly 10.

Abstract: A robot includes: a first arm rotatable about a first rotation axis; a second arm provided on the first arm rotatably about a second rotation axis that is a different axial direction from an axial direction of the first rotation axis; and a moving part provided on the second arm rotatably about a third rotation axis. The moving part has a third arm and a fourth arm. A maximum length of the moving part is longer than a length of the second arm and shorter than twice the length of the second arm. The first arm has a length longer than the length of the second arm. The first arm and the second arm can overlap with each other, as viewed from the axial direction of the second rotation axis.

Abstract: A robot system includes: a cell; and a robot which is provided to move in the cell, in which the robot includes an n-th (n is an integer which is equal to or greater than 1) arm which rotates around an n-th rotating axis, and an (n+1)th arm which is provided to rotate around an (n+1)th rotating axis which is an axial direction different from an axial direction of the n-th rotating axis, in the n-th arm, in which the length of the n-th arm is longer than the length of the (n+1)th arm, and in which, when viewed from the (n+1)th rotating axis, the n-th arm and the (n+1)th arm overlap each other.

Abstract: In an embodiment, a relative deflection detector may include at least two structural arcs, and a predetermined number of means for measuring position capable of determining the relative deflection in a first component. The at least two structural arcs may be for example, comprised of a first and second structural arc whereby the first and second structural arcs are attached to the first component at respective first and second predetermined locations and whereby each arc is comprised of a respective sequence of indicators, such as, for example, codes inscribed on the outer circumference of each arc. The first and second structural arcs may be positioned in concentric and coplanar relationship with each other.

Abstract: A robotic construction unit comprising a processor, a plurality of battery modules, and a plurality of magnetic modules. The processor is operable to control the operation of the magnetic modules. Each battery module is operable to provide power to at least one of the processor and a magnetic module of the plurality of magnetic modules. Each magnetic module is operable to alternatively establish magnetic attraction to a magnetic module of an adjacent robotic construction unit or establish magnetic repulsion to the magnetic module of the adjacent robotic construction unit.

Abstract: An apparatus and methods for training and/or operating a robotic device to follow a trajectory. A robotic vehicle may utilize a camera and stores the sequence of images of a visual scene seen when following a trajectory during training in an ordered buffer. Motor commands associated with a given image may be stored. During autonomous operation, an acquired image may be compared with one or more images from the training buffer in order to determine the most likely match. An evaluation may be performed in order to determine if the image may correspond to a shifted (e.g., left/right) version of a stored image as previously observed. If the new image is shifted left, right turn command may be issued. If the new image is shifted right then left turn command may be issued.

Abstract: Provided is a robot device including a drive unit including a plurality of links and joints connecting the links, a task instruction input unit for inputting an instruction of a task, a drive control unit for controlling an operation of the drive unit on the basis of the input task and determining a restricted area including a space necessary for the operation of the drive unit, and an area display unit for displaying the restricted area.

Abstract: Systems and methods for robotic path planning are disclosed. In some implementations of the present disclosure, a robot can generate a cost map associated with an environment of the robot. The cost map can comprise a plurality of pixels each corresponding to a location in the environment, where each pixel can have an associated cost. The robot can further generate a plurality of masks having projected path portions for the travel of the robot within the environment, where each mask comprises a plurality of mask pixels that correspond to locations in the environment. The robot can then determine a mask cost associated with each mask based at least in part on the cost map and select a mask based at least in part on the mask cost. Based on the projected path portions within the selected mask, the robot can navigate a space.

Abstract: A humanoid robot with a body joined to an omnidirectional mobile ground base, and equipped with: a body position sensor and a base position sensor to provide measures, actuators comprising at least 3 wheels located in the omnidirectional mobile base, extractors for converting the measures into useful data, a controller to calculate position, velocity and acceleration commands from the useful data using a robot model and pre-ordered position and velocity references, means for converting the commands into instructions for the actuators, wherein the robot model is a double point-mass model, and wherein the commands are based on a linear model predictive control law with a discretized time according to a sampling time period and a number of predicted samples, and expressed as a quadratic optimization formulation with: a weighted sum of objectives and a set of predefined linear constraints.

Abstract: Provided is a robot device including an image input unit for inputting an image of surroundings, a target object detection unit for detecting an object from the input image, an object position detection unit for detecting a position of the object, an environment information acquisition unit for acquiring surrounding environment information of the position of the object, an optimum posture acquisition unit for acquiring an optimum posture corresponding to the surrounding environment information for the object, an object posture detection unit for detecting a current posture of the object from the input image, an object posture comparison unit for comparing the current posture of the object to the optimum posture of the object, and an object posture correction unit for correcting the posture of the object when the object posture comparison unit determines that there is a predetermined difference or more between the current posture and the optimum posture.

Abstract: The invention is a system in which containers communicate their specifications to a robot, preferably a robotic arm, in order to teach the robot how to handle the individual contents of the containers. Each container has a controller that stores information about that container's contents. In order for the robot to interact with the container's contents, the robot communicates with the controller of the container to receive instructions for interacting with the contents. Preferably, the system is part of an automated storage and retrieval system, and the robot interacts with the contents of the containers as part of an assigned task, such as food preparation. The system may include feedback sensors and a user interface.

Abstract: The present application provides a control method and system, and a cleaning robot using the same. The control method comprises the following steps: under a navigation operating environment of the cleaning robot, controlling the image acquisition device to capture images in real time; analyzing at least one captured image; and controlling behaviors of the cleaning robot based on analyzed results and according to a preset cleaning mode, wherein the cleaning mode comprises a cleaning mode corresponding to an underexposure region. In the present application, users can clean some certain regions depending on requirements, thereby realizing the aim of separated-area cleaning according to the requirements of users.

Abstract: At least one tactile sensor includes an insulating layer and a conductive layer formed on the surface of the insulating layer. The conductive layer defines at least one group of flexible projections extending orthogonally from the surface of the insulating layer. The flexible projections include a major projection extending a distance orthogonally from the surface and at least one minor projection that is adjacent to and separate from the major projection wherein the major projection extends a distance orthogonally that is greater than the distance that the minor projection extends orthogonally. Upon a compressive force normal to, or a shear force parallel to, the surface, the major projection and the minor projection flex such that an electrical contact resistance is formed between the major projection and the minor projection. A capacitive tactile sensor is also disclosed that responds to the normal and shear forces.

Abstract: A system automatically loads a bin with a filled deformable container such as a sack of produce being conveyed along horizontal rollers. A movable support structure has a coupling end attachable to a robotic arm, and a lifting end supporting a plurality of parallel rods. By means of the robotic arm and a programmable logic controller, the plurality of parallel rods can be positioned between and parallel to the horizontal rollers, raised when the container is conveyed to a loading position above the parallel rods, moved to a predetermined position above the bin, and rotated to allow the container to slide downward along the parallel rods and into the bin under force of gravity. The loading sequence can be repeated a number of times, changing the predetermined position each time to stack a plurality of the containers in a desired configuration such as overlapping rows of offset sacks.