Used Universal Assembling Machine for sale (67,563)

Condition: reconditioned (used), Year of construction: 2014, Available immediately Moving column machine FS 480 - Total travel X=4800 mm, ideal for flexible machining of large parts - Travel X=4,800 mm, Y=1,500 mm; Z=3500 mm - iTNC 530 control with wireless HR 550 FS radio handwheel, operator's cabin on the traveling column - 2-axis NC universal drilling and milling head, fully simultaneous and positioning operation per traveling column Dedpfx Adjz Ipl Terecn - HSK-A 100 spindle, 10,000 rpm, 220 Nm spindle torque - IKZ air up to 6 bar - Dust protection packages to protect the guides and drives - BA 4 per traveling column - Radio measuring probe RMP 60 Renishaw - Work area monitoring with network camera and monitor at the rear of the system - Process monitoring ToolScope basic system - Additional control panel at the rear of the system - Partial enclosure consisting of work area and sheet metal door, rear with safety fence with unobstructed view into the work area - incl. fixators - Cooling units - incl. internal tool cooling (closed cooling circuit) with cooling unit - short delivery time, available immediately, subject to prior sale Inspection possible by arrangement Spindle hours: approx. 9079 SPECIAL PRICE!!!

Condition: reconditioned (used), Year of construction: 2014, Immediately available: Traveling column machine FS 1200 • Total travel X=12,000 mm, ideal for flexible large-scale machining • Travel X=12,000 mm, Y=1,500 mm; Z=3500mm • Control iTNC 530 with wireless radio handwheel HR 550 FS, operator cabin on the traveling column • 2-axis NC universal drilling, milling head, fully simultaneous and positioning operation per traveling column • Spindle HSK-A 100, 10,000 rpm, 220 Nm spindle torque • IKZ air up to 6 bar • Dust protection packages to protect the guides and drives • BA 4 per traveling column Dcsdpfx Adsz Ipmdersn • Radio measuring probe RMP 60, Renishaw make • Work area monitoring with network camera and monitor on the back of the system • Process monitoring ToolScope basic system • Additional control panel on the back of the system • Partial housing consisting of work area and sheet metal door, back with protective fence with a clear view into the work area • incl. fixators • Cooling units • incl. internal tool cooling (closed cooling circuit) with Cooling unit • short delivery time, available immediately, ---subject to prior sale--- Viewing possible by arrangement Spindle hours: approx. 9079 SPECIAL PRICE!

Condition: used, Year of construction: 2003, operating hours: 34,900 h, functionality: fully functional, machine/vehicle number: 112253, travel distance X-axis: 500 mm, travel distance Y-axis: 400 mm, travel distance Z-axis: 410 mm, controller model: Brother CNC-A00, total length: 2,250 mm, overall weight: 2,250 kg, spindle speed (max.): 12,000 rpm, number of slots in tool magazine: 26, BROTHER TC-22A – 5 AXIS - Manufacturer: Brother - Model: TC-22A - Serial Number: 112253 - Year: 2003 - Machine Type: CNC Vertical Machining / Tapping Center - CNC Control: Brother CNC-A00 - Number of Axes: 5 - X-Axis Travel: 500 mm - Y-Axis Travel: 400 mm - Z-Axis Travel: 410 mm - Table Size: 650 × 400 mm - Maximum Table Load: 200 kg - Distance Table to Spindle Nose: 200–610 mm - Spindle Taper: HSK-A40 - Spindle: 1 - Spindle Speed: up to 12,000 rpm standard - Tool Magazine: 26 tools - Maximum Tool Diameter: 55 mm - Maximum Tool Diameter with Adjacent Pockets Empty: 125 mm - Maximum Tool Length: 200 mm - Tool Change Time: approx. 0.7 sec Dodez Akqvopfx Adrocn - Rapid Traverse X/Y/Z: 56,000 mm/min - Spindle Motor: approx. 7.7 kW / 10 min rating - Power Supply: AC 200 V, 50/60 Hz - Maximum Power Requirement: 25 kVA - Rotary / Swivel Table: Installed - 5-Axis Configuration: 3 linear axes + 2 rotary/swivel axes - Coolant Treatment System: Included - Coolant / Lubricant Pump: Included - Machine Dimensions / Required Floor Space: approx. 1,671 × 2,846 mm - Machine Height: approx. 2,274 mm - Machine Weight: approx. 2,250 kg

Condition: reconditioned (used), Year of construction: 2010, • Traveling distances X=3100 mm, Y=1950 mm, Z=1390 mm • Heidenhain iTNC 530 with handwheel HR 410 Dodpfx Adez Ipl Hjrocn • Machine table for multi side working 3000 mm x 1600 mm • 2-axis NC-universal milling head, for simultaneous and positioning working • Spindel 10.000 U/min HSK 100, 130 Nm Spindle torque • Tool change system HSK 100 / 40 places for 750 mm long tools • Chip conveyor (screw type) in X-axis, for transport into • Chip conveyor scraper belt type (traverse conveyor), Fabr. Knoll • Coolant container 900 l, Fabr. Knoll • Outside air at spindle • IKZ 60 bar for deep hole drilling function • Covering with safety glass pane, open at the top for loading by crane • 2 part sliding doors at the operator side • 2 part sliding doors at the front side, for easy loading • Radio-controlled measuring probe RMP 60 • incl. washing gun • incl. podiums at the front side and operator side • complete factory overhauled and painted new • short time delivery after arrangement • used machine • Y-axis ball screw in September 2021 incl. bearings renewed • X-axis new linear guiding system, July 2023 changed, renewed • Spindle overhauled at Mai 2023 (clamping system new, clamping cartridge new, rotation unit new, general tests) (at 23105 spindle hours)) • can be visited under power at 72793 Pfullingen • optional fixators • optional installation at customers plant • optional transport • 23122 spindle hours in total • 53991 machine hours in total • Year of construction 2010 Subject to prior sale

Condition: used, Machine was regularly serviced, was in operation until recently, with documentation and accessories, an on-site inspection is possible. Dcsdpfx Aez Ibycsdrsn

Condition: used, Year of construction: 2018, Used, working condition unit. Additional details including pricing upon request. Dodpfsz Hlhhjx Adrjcn

Condition: good (used), Year of construction: 1997, Travel range X/Y/Z: 600mm/525mm/500mm Spindle speed: 20 - 6300 rpm, continuously variable and programmable Tool holder: SK40 Feed rate: max. 10m/min Rapid traverse rate X and Y axes: 18m/min Documentation available (see images) Upon request, transport and loading can be arranged throughout Europe for an additional fee. Prices plus VAT. Inspection possible by appointment. Contact us, our team will be happy to assist you. Dcjdjzxq D Ispfx Adron Machine buying and selling PURCHASE / SALE OF PRODUCTION & METALWORKING MACHINES, MACHINE TOOLS, ETC. Hob Awypjzvflhoakst Do you need a high-quality but affordable machine for your production? Or do you want to sell yours? For further information or to contact us, please use the contact form.

Condition: used, Control voltage: 42/48V, max. fuse rating: 35A, operating voltage: 380V, rated current: 20/22/24A, control: DECKEL DIALOG 11, an on-site inspection is possible. Dcjdpfx Ajz H Utmodrsn

Condition: good (used), Mikron WF 32 CH Universal Milling Machine Machine with chip and splash guard enclosure Equipped with a Heidenhain TNC355 control system Dcedpswit Rhefx Adron Technical Data Manufacturer: Mikron Type: WF 32 CH Control System: Heidenhain TNC355 Travel Ranges: X 560 mm, Y 500 mm, Z 400 mm Clamping Area: 530 x 900 mm Rapid Traverse Rates: X, Y 6,000 mm/min, Z 5,000 mm/min Spindle Speed: 20 – 6,300 rpm Dimensions: 2,700 x 2,000 x 2,400 mm Weight: 2,400 kg Heidenhain TNC355 Operating Manual Heidenhain TNC355 Programming Examples Heidenhain TNC 355 Service Manual More items – new and used – can be found in our shop! International shipping costs available upon request!

Condition: as good as new (ex-display), Year of construction: 2025, travel distance X-axis: 3,000 mm, travel distance Y-axis: 1,500 mm, travel distance Z-axis: 1,400 mm, rapid traverse X-axis: 30 m/min, rapid traverse Y-axis: 30 m/min, rapid traverse Z-axis: 30 m/min, workpiece weight (max.): 6,000 kg, rotational speed (max.): 10,000 rpm, tool length: 800 mm, New machine HDC3000 with 6 axes • Travel ranges: X=3000 mm, Y=1500 mm, Z=1400 mm • Heidenhain iTNC 640 with handwheel • NC rotary table for 5-sided machining 1250 mm x 1600 mm • 2-axis NC universal drilling and milling head, fully simultaneous and positioning operation • Spindle 10,000 rpm HSK100, S1=220 Nm spindle torque • Tool change system HSK100 / 60 stations – 800 mm tool length • Chip conveyor • Optimized for 5-sided machining including deep hole drilling • Coolant supply system • Internal/external air blow-off device • ICS 60 bar for deep hole machining • Fully enclosed • Large interference circle 2300 mm • Including mounts • Including wash gun • Including warranty • Short delivery time, subject to prior sale Dcedpoz Ipnzjfx Adren

Condition: used, Year of construction: 1987, Technical details: x-travel: 700 mm y-travel: 500 mm z-travel: 600 mm table swivelling +/-: A-Achse: 20° / 60° Grad table rotating: B-Achse: 360° Grad control: Maho 432 (3-D Bahnsteuerung) Max. Milling-capacity: ST: 60 und GG: 22 mm tool changer with: 24 Plätze number of spindle speeds: 20 - 6300 U/min. max. table load: 200 kg spindle taper MT: ISO 40 (hydr. Spannung) spindle head swivable left - right: 90° (manuell) ° quill stroke: 80 mm feed range: X/Z: 1 - 3000 und Y: 1 - 4000 und B: 0,1 - 3000°/min. mm/min rapid traverse:: X/Z: 10 und Y: 8 und B: 20 U/min. m/min control voltage: 110/220 V total power requirement: ca. 20 kVA Weight approx.: 5,5 t dimension machine xH: 3,0 x 2,4 x 2,25 m space requirements of the machine approx.: 5,2 x 5,0 x H: 2,3 m NC rotary table Ø 520 mm with A and B axes Adjustable three-phase motor with 4-stage reduction gear Working spindle can be swiveled out for horizontal spindle Equipment: -manual control unit -coolant device -machine ilumination Dsdpeu Idbysfx Adrjcn *

Condition: used, Year of construction: 2014, functionality: fully functional, Milling swivel head: - with torque motor and hydraulic clamping - Swivel range +30/-120°, stepless - 14,000 RPM - 160 Nm torque - Drive power 29 kW - Separate spindle cooling for constant temperature - Tool holder DIN SK40 with air blow-out function Integrated rotary table: - with torque motor and hydraulic clamping - Ø 610 mm - Extended clamping area 1,100 x 610 mm General: - 40-position tool changer with dual-arm gripper - Coolant and compressed air gun - Chip conveyor - Coolant system - Electronic handwheel - Work area light Control system: Heidenhain iTnc 530 SmarT.NC HSCI - 15.1'' TFT screen Dedpfxszzp E Nj Adrscn - Ethernet interface - 2x USB port - SmarT.NC-guided programming - Plain text programming - Short sentence processing time - Create a new program while another is being processed - Proven Heidenhain machining cycles - CE certification Options: - Internal cooling system (IKZ), 40 bar, including band filter system - Heidenhain TS640 for DIN SK40 workpiece probing system with infrared transmission - Heidenhain software option 40: DCM Dynamic Collision Monitoring for iTNC 530 - Heidenhain KinematicsOpt incl. Heidenhain calibration sphere KKH 250

Condition: good (used), Year of construction: 2019, Universal machining center Machine type: Hedelius Acura 65 Control: Heidenhain TNC 640 Year: 2019 Available after: Dezember 2026 SPECIFICATIONS 5-axis-simultaneous X-Axis: 700 mm Y-Axis: 650 / 465 mm Z-Axis: 600 mm Rapid motion: (X/Y/Z): 40/40/40 m/min. Dodjz D Aq Ujpfx Adrjcn B-Axes: +30° / -115° Spindle speeds: 12.000 rpm Spindle power: 22 kW Torque: 117 Nm Tool: SK 40 Tool capacity: 65 Table size: D: 650 x 540 mm mm Max. Table Load: 500 kg Equipment Chip conveyor 3D-Touch probe: M&H Internal cooling: 25 bar Cooling tank: 500 l Electronical handwheel: HR 510 Oil mist separator Chip rinsing pistol Kinematikset 3D-Formenbauabstimmung Documentation - German

Condition: used, Year of construction: 1989, x-travel 400 mm y-travel 400 mm z-travel 400 mm table surface area 700 x 460 mm spindle taper SK 40 Dcsdez Ekzkopfx Adrjn spindle turning speed range 31,5 -5000 U/min spindle drive 5,5 kW quill stroke 80 mm vertical head swivelling +/- 90 ° control DIALOG 11 feeds x/y/z -stepless 3000 mm/min rapid traverse 6 m/min total power requirement 13,8 kVA weight of the machine ca. 2 t dimensions of machine L x W x H 2,73 x 2,0 x 2,0 m Accessories: solid table, vertical head with hydr. tool clamping and quil retraction, dividing unit HOFFMANN, RW/NC 125 L, coolant

Condition: used, Year of construction: 2013, Working condition machines. Feeders included. Used: 8mm doble – 63 pcs. 12 mm – 40 pcs 24/32 mm – 13 pcs Dcodez Du Skjpfx Adrsn Stick feeder – 2 pcs Tape feeder 12 mm – 1 pcs Tape feeder 8 mm – 1 pcs Tape feeder 44/56 mm – 1 pcs New ones: Stick feeder – 1 pcs Tape feeder 44/56 mm – 3 pcs Tape feeder 24/32 mm – 5 pcs

Condition: excellent (used), Year of construction: 2020, functionality: fully functional, We offer you: CNC bed milling machine Manufacturer: DMG MORI Type: DMF 360-11 Year of construction: 2020 Control system: Celos with Siemens 840D sl Operate Technical data: Travel ranges: X-axis: 3,600 mm Y-axis: 1,100 mm Dcjdpfoz A Ap Isx Adron Z-axis: 900 mm Main spindle: Speed range - main spindle: 20 - 15,000 rpm Drive power - main spindle (100/40%): 46 / 30 kW Torque: 200 / 130 Nm Work table: Table clamping surface: 4,200 x 1,100 mm Rotary table: d 1,050 mm Max. table load: 1,200 kg Tool changer: Number of tool positions: 120 Tool holder: HSK-A 63 Feeds: Rapid traverse (x/y/z): 40 / 40 / 40 m/min Operating hours: approx. 23,850 h Spindle hours: approx. 11,500 h Technical features & accessories: - 5-axis simultaneous machining - NC swivel milling head (B-axis) - Integrated rotary table, arranged on the left, hydraulically clamped - Full enclosure - Coolant tank - Direct measuring systems - Drag chain chip conveyor - Internal coolant supply (IKZ) 40 bar, includes: - Paper band filter, 600 l - 2 rotating viewing windows - Purge air for linear measuring systems - Rotary coupling for spindle - Flushing gun for chip flushing - 2x oil and emulsion mist separators - Blow-off air through the spindle center - Infrared measuring probe, Heidenhain TS 460 (if available) - Preparation for 3D quickSET - MPC – Machine Protection Control - Operating mode 4 - ATC (Application Tuning Cycle) - Preparation for Hofmann dividing head RW-NC 300 (dividing head not included) - Alternating operation - Tool breakage monitoring TRS2 - Tracy surface interpolation Accessories, tools and clamping devices shown in the pictures are only included in the scope of supply if this is stated in the additional information. Subject to changes and errors in the technical data and information, as well as prior sale!

Condition: excellent (used), with internal grinding attachment Center height 125 mm Distance between centers 1000 mm Table size 1650 x 145 mm Grinding wheel 400 x 50 x 127 mm Grinding wheel speeds 1'500 - 2'200 rpm Grinding head turnable 270° Grinding wheel 225 x 20 x 76.2 mm Misc. accessories Dcedpfx Adey H Dq Horen MARCELS MASCHINEN AG

Condition: good (used), Year of construction: 2011, functionality: fully functional, We offer you: CNC machining center, universal Manufacturer: DMG MORI Type: DMU 80 P duoBlock Year of construction: 2011 Control system: Heidenhain iTNC 530 Technical data: Travel ranges: X-axis: 800 mm Y-axis: 1,050 mm Z-axis: 800 mm Main spindle: Max. spindle speed: 18,000 rpm Rotary table: Table diameter: d 900 x 700 mm Tool changer: Dcodpfx Aez Ebzujdron Tool holder: HSK-A63 Number of tool positions: 60 Operating hours: approx. 49,285 h Spindle hours: approx. 15,380 h Technical features & accessories: - Universal milling head with controlled B-axis - Coolant tank 500 l - Internal coolant supply 40 bar - Chip conveyor with integrated fabric band filter - Rotating viewing window - Infrared measuring probe, manufacturer Heidenhain TS 649 (if available) - Preparation for 3D quickSET - Signal tower, 4 colors - Flushing gun - Cooling system with compressed air through the spindle center - Electronic handwheel (if available) - Operating mode 4 Accessories, tools and clamping devices shown in the pictures are only included in the scope of delivery if this is stated in the additional information. Subject to changes and errors in the technical data and information, as well as prior sale!

Condition: good (used), Year of construction: 1990, 1 used, well-maintained CNC tool milling machine, traveling column design, with CNC path control GRUNDIG Dialog 11 Table size 1600 x 675 mm Tool holder SK / ISO 40 Travel distances X-axis, longitudinal 1200 mm Y-axis, transverse 600 mm Z-axis, vertical 500 mm Table load 2000 kg Spindle speed range 20 – 6300 rpm Feed rate range, stepless 2 – 10,000 mm/min Rapid traverse in all axes 10 m/min Quill stroke 80 mm Drive power 100% ED 7.5 kW 40% ED 12 kW Machine dimensions L x W x H 3600 x 3000 x 2300 mm Machine weight 6800 kg Control cabinet dimensions L x W x H 1700 x 900 x 1750 mm Control cabinet weight 470 kg Accessories / Special features: • CNC tool milling machine suitable for tool and fixture manufacturing, training, and mold making • CNC path control GRUNDIG Dialog 11 • Screen graphics, dialog-guided input, 3D linear interpolation, circular interpolation, helical interpolation, polar coordinate input, numerous drilling and milling cycles, cycle input graphically supported, milling cycles "contour pocket" for automatic free milling of irregular pockets, even with islands, shifting and rotation of the coordinate system • Electronic handwheel • RS 232 interface Dodpfx Adshhuf Hsrjcn • Swiveling vertical milling head +/- 90° • Hydraulic tool clamping, DIN 2080 with clamping groove, Ott system • Quill adjustment 80 mm • Horizontal milling attachment • Full protection enclosure • Ball screw spindles in all 3 axes • Coolant system • Lighting Siegfried Volz Werkzeugmaschinen Rüschebrinkstr. 151-153 D - 44143 Dortmund - Wambel

Condition: excellent (used), Year of construction: 2019, functionality: fully functional, We offer you: Manufacturer: DMG MORI Type: DMU 95 monoBlock Year of manufacture: 2019 Control system: Siemens 840D sl Operate Technical data: Travel distances: Dedpsz Ap N Djfx Adrocn X-axis: 950 mm Y-axis: 850 mm Z-axis: 650 mm Rotational range C-axis: 360° Swivel range A-axis: +/- 120° Main spindle: Tool interface: HSK-63A Speed range - main spindle: 20,000 rpm Drive power - main spindle (100/40%): 35 / 25 kW Torque: 130 / 86 Nm Rotary table: Table dimensions: C-axis d850 x 750 mm integrated into Fixed table 1,000 mm x 750 mm Max. table load: 1,000 kg Max. workpiece dimensions: d 1,040 mm (clamping)/ d 850 mm (machinable) h 590 mm Tool changer: Number of tool positions: 60 Max. tool diameter: 80 / 160 mm Max. tool length: 420 mm Max. tool weight: 8 kg Chip-to-chip change time: 5.9 s Feed rates: Rapid traverse (x/y/z): 40 m/min Feed rate (x/y/z): 40,000 mm/min Technical features & accessories: - Tool changer system with dual gripper - MPC Machine Protection Control - Production package: - Chip conveyor with coolant unit 600 l / 160 gallons, - Paper band filter - Internal coolant supply, 40 bar / 23 l/min, through the spindle center (AD) - External coolant supply, 4 bar – 40 l/min, (theoretical pump capacity) - Chip flushing in the cabinet door (no standard coolant unit) - Spray gun 3 bar – 40 l/min - Oil and emulsion mist separator, mechanical filter, flow rate 600 m³/h - Infrared measuring probe Renishaw PP60 optical (OMP 60) (if available) - Blum laser, tool measurement in the machining area - 3D quickSET preparation - Electronic handwheel (if available) Accessories, tools and clamping devices shown in the pictures are only included in the scope of supply if this is stated in the additional information. Subject to change and errors in technical data and specifications, as well as prior sale!

Condition: used, Year of construction: 2004, x-travel 4000 mm y-travel 1200 mm z-travel 1500 mm table-size 4200 x 1100 mm tool adaptor SK 50 | turning speed range 5000 U/min power requirement 37 kW control Heidenhain iTNC 530 table load 6,0 t milling head -swivable A= 1,0°/ B= 1,0° Grad tool change unit 60 SK 50 range L-W-H 11,0 x 5,0 x 4,0 m Universale CNC- bed milling machine with extra round table H/V - internal coolant - filter system - oil cooler - external handwheel Dcsdpez It Dtefx Adron - chipconveyor

Condition: excellent (used), Year of construction: 2019, 5-axis machining center POS POSMILL H 800 U Control: Heidenhain iTNC 530 Year of manufacture: 2019 Internal machine number: 40 ATTENTION: Machine has ONLY 500 spindle hours!!! Travel distances: X-axis: 670 mm Y-axis: 830 mm Z-axis: 600 mm A +120° to -120°, C 360° Table load: 1,200 kg Tool holder: HSK-63A Tool magazine: 96 positions Spindle speed: 18,000 rpm Equipment Rotary swivel table Rotating viewing window Glass scales in all axes Handheld control unit Heidenhain measuring probe Laser for tool breakage detection Rotary through-spindle in the table Air connection in the table incl. M-function Coolant system Internal cooling Chip conveyor Automatic roof Extraction system Documentation General data Repeatability/positioning accuracy upon new delivery 0.004 mm/0.008 mm (VDI/DGQ 3441) incl. tool holders with tools on the tool changer, (No suggestions), oil mist extraction IKZ (Internal Coolant System) Chip conveyor Rated power 90 kVA Full load current 125 A Max. current load 200 A 400 V 50 Hz Djdpfx Asyk Az Djdrjcn

Year of construction: 1988, condition: used, Rated current: 25A, control voltage: 24V, operating voltage: 380V, control: DECKEL Dialog 2, weight: approx. 1.8t, without clamping systems or tools, Z-axis scale defective, screen display partially incorrect, not operational, an on-site inspection is possible. Dodpfx Asz Ea Sfjdrocn

Condition: used, Year of construction: 1985, Technical details: x-travel: 485 mm y-travel: 385 mm z-travel: 380 mm control: Contour 1 Bahnsteuerung spindle taper ISO: SK 40 spindle head swivable left - right: 90° ° quill travel: 80 mm milling head vertical adjustable: 150 ( y-Achse) mm range of revolution per miute: Spindel vertical: 50 - 2.500 / 18 step U/min feed:: X/Y/Z: 2 - 1000 steples mm/min rapid traverse : X/Y/Z: 2000 mm/min revolution per minute: horizontal: bis 1.000 U/min Table dimensions: 460 x 800 mm table load: 0,4 t total power requirement: 9,5 kVA machine weight approx.: 1900 kg dimension machine xH: 2,35 x 2,2 x 2,0 m -Equipment: - Operation via control panel Grundig elektronic with boom - Cooling with pump - machine lighting - Linear interpolation, circular polarization in XY and XZ planes - quick chuck - manual control unit Dedpju Ndcmjfx Adrecn *

Condition: used, Year of construction: 2007, Technical details: x-travel: 1000 mm y-travel: 1000 mm z-travel: 500 mm B-axis (table): 360 ° spindle taper: HSK A63 working spindle range of revolution per minute : 15000 U/min rotary table: 260 mm control: Andronic 2060PKM Dcedpfx Aou Idm Nodren feed: 1 - 5000 mm/min rapid traverse X,Y: 15 m/min. rapid traverse Z-axis: 12 m/min total power requirement: ca. 42 kW weight of the machine ca.: 6,0 t dimensions electric cabinet LxWxH: 2,4x0,6x2,2 m dimension machine xH: 3,5x2,4x3,2 m 5-axis BAZ in parallel kinematics suitable for prototypes. i.D. *