Global Ultra-thin Six-Dimensional Force Sensor Market 2026 by Manufacturers, Regions, Type and Application, Forecast to 2032
1 Market Overview
- 1.1 Product Overview and Scope
- 1.2 Market Estimation Caveats and Base Year
- 1.3 Market Analysis by Type
- 1.3.1 Overview: Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Type: 2021 Versus 2025 Versus 2032
- 1.3.2 Strain Gaug
- 1.3.3 Piezoelectric
- 1.3.4 Capacitive
- 1.3.5 Others
- 1.4 Market Analysis by Supply Voltage
- 1.4.1 Overview: Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Supply Voltage: 2021 Versus 2025 Versus 2032
- 1.4.2 5V
- 1.4.3 12V
- 1.4.4 24V
- 1.5 Market Analysis by Application
- 1.5.1 Overview: Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Application: 2021 Versus 2025 Versus 2032
- 1.5.2 Robots
- 1.5.3 Aerospace
- 1.5.4 Automotive
- 1.5.5 Medical
- 1.5.6 Others
- 1.6 Global Ultra-thin Six-Dimensional Force Sensor Market Size & Forecast
- 1.6.1 Global Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021 & 2025 & 2032)
- 1.6.2 Global Ultra-thin Six-Dimensional Force Sensor Sales Quantity (2021-2032)
- 1.6.3 Global Ultra-thin Six-Dimensional Force Sensor Average Price (2021-2032)
2 Manufacturers Profiles
- 2.1 ATI Industrial Automation
- 2.1.1 ATI Industrial Automation Details
- 2.1.2 ATI Industrial Automation Major Business
- 2.1.3 ATI Industrial Automation Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.1.4 ATI Industrial Automation Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.1.5 ATI Industrial Automation Recent Developments/Updates
- 2.2 Schunk
- 2.2.1 Schunk Details
- 2.2.2 Schunk Major Business
- 2.2.3 Schunk Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.2.4 Schunk Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.2.5 Schunk Recent Developments/Updates
- 2.3 Nidec
- 2.3.1 Nidec Details
- 2.3.2 Nidec Major Business
- 2.3.3 Nidec Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.3.4 Nidec Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.3.5 Nidec Recent Developments/Updates
- 2.4 MareX Ltd
- 2.4.1 MareX Ltd Details
- 2.4.2 MareX Ltd Major Business
- 2.4.3 MareX Ltd Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.4.4 MareX Ltd Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.4.5 MareX Ltd Recent Developments/Updates
- 2.5 Longlv Electronic
- 2.5.1 Longlv Electronic Details
- 2.5.2 Longlv Electronic Major Business
- 2.5.3 Longlv Electronic Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.5.4 Longlv Electronic Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.5.5 Longlv Electronic Recent Developments/Updates
- 2.6 Robot Maxpower
- 2.6.1 Robot Maxpower Details
- 2.6.2 Robot Maxpower Major Business
- 2.6.3 Robot Maxpower Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.6.4 Robot Maxpower Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.6.5 Robot Maxpower Recent Developments/Updates
- 2.7 Sunrise Instruments
- 2.7.1 Sunrise Instruments Details
- 2.7.2 Sunrise Instruments Major Business
- 2.7.3 Sunrise Instruments Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.7.4 Sunrise Instruments Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.7.5 Sunrise Instruments Recent Developments/Updates
- 2.8 Kunwei Sensing Technology
- 2.8.1 Kunwei Sensing Technology Details
- 2.8.2 Kunwei Sensing Technology Major Business
- 2.8.3 Kunwei Sensing Technology Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.8.4 Kunwei Sensing Technology Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.8.5 Kunwei Sensing Technology Recent Developments/Updates
- 2.9 Starsin Sensing Technology
- 2.9.1 Starsin Sensing Technology Details
- 2.9.2 Starsin Sensing Technology Major Business
- 2.9.3 Starsin Sensing Technology Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.9.4 Starsin Sensing Technology Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.9.5 Starsin Sensing Technology Recent Developments/Updates
- 2.10 Hypersen
- 2.10.1 Hypersen Details
- 2.10.2 Hypersen Major Business
- 2.10.3 Hypersen Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.10.4 Hypersen Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.10.5 Hypersen Recent Developments/Updates
- 2.11 Link-Touch
- 2.11.1 Link-Touch Details
- 2.11.2 Link-Touch Major Business
- 2.11.3 Link-Touch Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.11.4 Link-Touch Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.11.5 Link-Touch Recent Developments/Updates
- 2.12 XJCSENSOR
- 2.12.1 XJCSENSOR Details
- 2.12.2 XJCSENSOR Major Business
- 2.12.3 XJCSENSOR Ultra-thin Six-Dimensional Force Sensor Product and Services
- 2.12.4 XJCSENSOR Ultra-thin Six-Dimensional Force Sensor Sales Quantity, Average Price, Revenue, Gross Margin and Market Share (2021-2026)
- 2.12.5 XJCSENSOR Recent Developments/Updates
3 Competitive Environment: Ultra-thin Six-Dimensional Force Sensor by Manufacturer
- 3.1 Global Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Manufacturer (2021-2026)
- 3.2 Global Ultra-thin Six-Dimensional Force Sensor Revenue by Manufacturer (2021-2026)
- 3.3 Global Ultra-thin Six-Dimensional Force Sensor Average Price by Manufacturer (2021-2026)
- 3.4 Market Share Analysis (2025)
- 3.4.1 Producer Shipments of Ultra-thin Six-Dimensional Force Sensor by Manufacturer Revenue ($MM) and Market Share (%): 2025
- 3.4.2 Top 3 Ultra-thin Six-Dimensional Force Sensor Manufacturer Market Share in 2025
- 3.4.3 Top 6 Ultra-thin Six-Dimensional Force Sensor Manufacturer Market Share in 2025
- 3.5 Ultra-thin Six-Dimensional Force Sensor Market: Overall Company Footprint Analysis
- 3.5.1 Ultra-thin Six-Dimensional Force Sensor Market: Region Footprint
- 3.5.2 Ultra-thin Six-Dimensional Force Sensor Market: Company Product Type Footprint
- 3.5.3 Ultra-thin Six-Dimensional Force Sensor Market: Company Product Application Footprint
- 3.6 New Market Entrants and Barriers to Market Entry
- 3.7 Mergers, Acquisition, Agreements, and Collaborations
4 Consumption Analysis by Region
- 4.1 Global Ultra-thin Six-Dimensional Force Sensor Market Size by Region
- 4.1.1 Global Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Region (2021-2032)
- 4.1.2 Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Region (2021-2032)
- 4.1.3 Global Ultra-thin Six-Dimensional Force Sensor Average Price by Region (2021-2032)
- 4.2 North America Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021-2032)
- 4.3 Europe Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021-2032)
- 4.4 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021-2032)
- 4.5 South America Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021-2032)
- 4.6 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Consumption Value (2021-2032)
5 Market Segment by Type
- 5.1 Global Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 5.2 Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Type (2021-2032)
- 5.3 Global Ultra-thin Six-Dimensional Force Sensor Average Price by Type (2021-2032)
6 Market Segment by Application
- 6.1 Global Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 6.2 Global Ultra-thin Six-Dimensional Force Sensor Consumption Value by Application (2021-2032)
- 6.3 Global Ultra-thin Six-Dimensional Force Sensor Average Price by Application (2021-2032)
7 North America
- 7.1 North America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 7.2 North America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 7.3 North America Ultra-thin Six-Dimensional Force Sensor Market Size by Country
- 7.3.1 North America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Country (2021-2032)
- 7.3.2 North America Ultra-thin Six-Dimensional Force Sensor Consumption Value by Country (2021-2032)
- 7.3.3 United States Market Size and Forecast (2021-2032)
- 7.3.4 Canada Market Size and Forecast (2021-2032)
- 7.3.5 Mexico Market Size and Forecast (2021-2032)
8 Europe
- 8.1 Europe Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 8.2 Europe Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 8.3 Europe Ultra-thin Six-Dimensional Force Sensor Market Size by Country
- 8.3.1 Europe Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Country (2021-2032)
- 8.3.2 Europe Ultra-thin Six-Dimensional Force Sensor Consumption Value by Country (2021-2032)
- 8.3.3 Germany Market Size and Forecast (2021-2032)
- 8.3.4 France Market Size and Forecast (2021-2032)
- 8.3.5 United Kingdom Market Size and Forecast (2021-2032)
- 8.3.6 Russia Market Size and Forecast (2021-2032)
- 8.3.7 Italy Market Size and Forecast (2021-2032)
9 Asia-Pacific
- 9.1 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 9.2 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 9.3 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Market Size by Region
- 9.3.1 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Region (2021-2032)
- 9.3.2 Asia-Pacific Ultra-thin Six-Dimensional Force Sensor Consumption Value by Region (2021-2032)
- 9.3.3 China Market Size and Forecast (2021-2032)
- 9.3.4 Japan Market Size and Forecast (2021-2032)
- 9.3.5 South Korea Market Size and Forecast (2021-2032)
- 9.3.6 India Market Size and Forecast (2021-2032)
- 9.3.7 Southeast Asia Market Size and Forecast (2021-2032)
- 9.3.8 Australia Market Size and Forecast (2021-2032)
10 South America
- 10.1 South America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 10.2 South America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 10.3 South America Ultra-thin Six-Dimensional Force Sensor Market Size by Country
- 10.3.1 South America Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Country (2021-2032)
- 10.3.2 South America Ultra-thin Six-Dimensional Force Sensor Consumption Value by Country (2021-2032)
- 10.3.3 Brazil Market Size and Forecast (2021-2032)
- 10.3.4 Argentina Market Size and Forecast (2021-2032)
11 Middle East & Africa
- 11.1 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Type (2021-2032)
- 11.2 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Application (2021-2032)
- 11.3 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Market Size by Country
- 11.3.1 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Sales Quantity by Country (2021-2032)
- 11.3.2 Middle East & Africa Ultra-thin Six-Dimensional Force Sensor Consumption Value by Country (2021-2032)
- 11.3.3 Turkey Market Size and Forecast (2021-2032)
- 11.3.4 Egypt Market Size and Forecast (2021-2032)
- 11.3.5 Saudi Arabia Market Size and Forecast (2021-2032)
- 11.3.6 South Africa Market Size and Forecast (2021-2032)
12 Market Dynamics
- 12.1 Ultra-thin Six-Dimensional Force Sensor Market Drivers
- 12.2 Ultra-thin Six-Dimensional Force Sensor Market Restraints
- 12.3 Ultra-thin Six-Dimensional Force Sensor Trends Analysis
- 12.4 Porters Five Forces Analysis
- 12.4.1 Threat of New Entrants
- 12.4.2 Bargaining Power of Suppliers
- 12.4.3 Bargaining Power of Buyers
- 12.4.4 Threat of Substitutes
- 12.4.5 Competitive Rivalry
13 Raw Material and Industry Chain
- 13.1 Raw Material of Ultra-thin Six-Dimensional Force Sensor and Key Manufacturers
- 13.2 Manufacturing Costs Percentage of Ultra-thin Six-Dimensional Force Sensor
- 13.3 Ultra-thin Six-Dimensional Force Sensor Production Process
- 13.4 Industry Value Chain Analysis
14 Shipments by Distribution Channel
- 14.1 Sales Channel
- 14.1.1 Direct to End-User
- 14.1.2 Distributors
- 14.2 Ultra-thin Six-Dimensional Force Sensor Typical Distributors
- 14.3 Ultra-thin Six-Dimensional Force Sensor Typical Customers
15 Research Findings and Conclusion
16 Appendix
- 16.1 Methodology
- 16.2 Research Process and Data Source
According to our (Global Info Research) latest study, the global Ultra-thin Six-Dimensional Force Sensor market size was valued at US$ 71.21 million in 2025 and is forecast to a readjusted size of US$ 380 million by 2032 with a CAGR of 27.0% during review period.
In 2025, global Ultra-thin Six-Dimensional Force Sensor production reached approximately 14k units , with an average global market price of around US$5k per unit.
An Ultra-thin Six-Dimensional Force Sensor is a high-precision multi-axis force/torque sensor capable of simultaneously measuring three orthogonal force components and three torque components in three-dimensional space, namely Fx, Fy, Fz and Mx, My, Mz. Compared with conventional six-dimensional force sensors, ultra-thin six-dimensional force sensors feature a thinner profile, more compact structure, lower installation height, faster response, and better suitability for embedded integration. They are particularly suitable for robotic end effectors, collaborative robot joints, humanoid robot wrists, precision assembly, force-controlled grinding and polishing, medical robots, aerospace testing, and semiconductor manufacturing equipment where limited installation space and high measurement accuracy are required. These products typically use elastic structures, strain gauges, bridge circuits, MEMS sensing elements, piezoelectric elements, or optical fiber sensing technologies to convert multi-directional forces into electrical signals, and then output six-axis force/torque data through decoupling algorithms and signal-conditioning modules. They are core sensing components for robotic force control, intelligent perception, and precision manufacturing.
The upstream supply chain of Ultra-thin Six-Dimensional Force Sensors mainly includes elastomer materials such as stainless steel, aluminum alloy, titanium alloy, and high-strength alloy steel, as well as strain gauges, MEMS chips, piezoelectric ceramics, fiber Bragg gratings, adhesives, flexible printed circuits, signal-conditioning chips, ADC converters, connectors, packaging materials, precision machining equipment, and calibration equipment. Material properties, strain-gauge consistency, chip accuracy, machining precision, temperature-drift control, and calibration algorithms directly affect sensor sensitivity, linearity, coupling error, and long-term stability. Representative upstream suppliers include Vishay, HBK, TE Connectivity, Analog Devices, Texas Instruments, STMicroelectronics, Infineon, Murata, TDK, Kyocera, Nippon Steel, Baosteel, Constellium, and Kobe Steel. The midstream sector consists of multi-axis force sensor manufacturers, robot sensor companies, precision measurement instrument suppliers, and industrial automation component providers responsible for elastomer structure design, sensing element bonding, signal acquisition, decoupling algorithms, calibration testing, and product packaging. Downstream applications mainly include collaborative robots, industrial robots, humanoid robots, medical robots, semiconductor equipment, precision assembly, aerospace testing, automotive testing, force-controlled grinding and polishing, scientific research, and automated production lines. Representative application companies include ABB, FANUC, Yaskawa, KUKA, Universal Robots, Doosan Robotics, Tesla, Figure AI, Agility Robotics, Boston Dynamics, Intuitive Surgical, Stryker, Applied Materials, ASML, Tokyo Electron, Teradyne, Siemens, Bosch, and Foxconn.
The Ultra-thin Six-Dimensional Force Sensor market is currently experiencing rapid growth driven by increasing demand for robotic intelligence and precision force control. Collaborative robots, humanoid robots, medical robots, semiconductor equipment, and precision assembly are the main growth directions. Key trends include thinner profiles, miniaturization, higher accuracy, lower coupling error, digital output, improved anti-interference capability, and deeper integration with robot control systems. Market growth is driven by increasing use of robotic force control, flexible manufacturing development, rising interest in humanoid robots, growing demand for precise tactile sensing in medical and semiconductor equipment, and domestic substitution in high-end sensors. Major challenges include difficult high-precision calibration, strict production consistency requirements, high barriers in core algorithms and manufacturing processes, long customer validation cycles, high product prices, and the continued dominance of a few international brands in the high-end market. Overall, the market is expected to expand from research and high-end industrial applications toward broader batch adoption in collaborative robots, humanoid robots, and intelligent manufacturing.
This report is a detailed and comprehensive analysis for global Ultra-thin Six-Dimensional Force Sensor market. Both quantitative and qualitative analyses are presented by manufacturers, by region & country, by Type and by Application. As the market is constantly changing, this report explores the competition, supply and demand trends, as well as key factors that contribute to its changing demands across many markets. Company profiles and product examples of selected competitors, along with market share estimates of some of the selected leaders for the year 2025, are provided.
Key Features:
Global Ultra-thin Six-Dimensional Force Sensor market size and forecasts, in consumption value ($ Million), sales quantity (K Units), and average selling prices (US$/Unit), 2021-2032
Global Ultra-thin Six-Dimensional Force Sensor market size and forecasts by region and country, in consumption value ($ Million), sales quantity (K Units), and average selling prices (US$/Unit), 2021-2032
Global Ultra-thin Six-Dimensional Force Sensor market size and forecasts, by Type and by Application, in consumption value ($ Million), sales quantity (K Units), and average selling prices (US$/Unit), 2021-2032
Global Ultra-thin Six-Dimensional Force Sensor market shares of main players, shipments in revenue ($ Million), sales quantity (K Units), and ASP (US$/Unit), 2021-2026
The Primary Objectives in This Report Are:
To determine the size of the total market opportunity of global and key countries
To assess the growth potential for Ultra-thin Six-Dimensional Force Sensor
To forecast future growth in each product and end-use market
To assess competitive factors affecting the marketplace
This report profiles key players in the global Ultra-thin Six-Dimensional Force Sensor market based on the following parameters - company overview, sales quantity, revenue, price, gross margin, product portfolio, geographical presence, and key developments. Key companies covered as a part of this study include ATI Industrial Automation, Schunk, Nidec, MareX Ltd, Longlv Electronic, Robot Maxpower, Sunrise Instruments, Kunwei Sensing Technology, Starsin Sensing Technology, Hypersen, etc.
This report also provides key insights about market drivers, restraints, opportunities, new product launches or approvals.
Market Segmentation
Ultra-thin Six-Dimensional Force Sensor market is split by Type and by Application. For the period 2021-2032, the growth among segments provides accurate calculations and forecasts for consumption value by Type, and by Application in terms of volume and value. This analysis can help you expand your business by targeting qualified niche markets.
Market segment by Type
Strain Gaug
Piezoelectric
Capacitive
Others
Market segment by Supply Voltage
5V
12V
24V
Market segment by Application
Robots
Aerospace
Automotive
Medical
Others
Major players covered
ATI Industrial Automation
Schunk
Nidec
MareX Ltd
Longlv Electronic
Robot Maxpower
Sunrise Instruments
Kunwei Sensing Technology
Starsin Sensing Technology
Hypersen
Link-Touch
XJCSENSOR
Market segment by region, regional analysis covers
North America (United States, Canada, and Mexico)
Europe (Germany, France, United Kingdom, Russia, Italy, and Rest of Europe)
Asia-Pacific (China, Japan, Korea, India, Southeast Asia, and Australia)
South America (Brazil, Argentina, Colombia, and Rest of South America)
Middle East & Africa (Saudi Arabia, UAE, Egypt, South Africa, and Rest of Middle East & Africa)
The content of the study subjects, includes a total of 15 chapters:
Chapter 1, to describe Ultra-thin Six-Dimensional Force Sensor product scope, market overview, market estimation caveats and base year.
Chapter 2, to profile the top manufacturers of Ultra-thin Six-Dimensional Force Sensor, with price, sales quantity, revenue, and global market share of Ultra-thin Six-Dimensional Force Sensor from 2021 to 2026.
Chapter 3, the Ultra-thin Six-Dimensional Force Sensor competitive situation, sales quantity, revenue, and global market share of top manufacturers are analyzed emphatically by landscape contrast.
Chapter 4, the Ultra-thin Six-Dimensional Force Sensor breakdown data are shown at the regional level, to show the sales quantity, consumption value, and growth by regions, from 2021 to 2032.
Chapter 5 and 6, to segment the sales by Type and by Application, with sales market share and growth rate by Type, by Application, from 2021 to 2032.
Chapter 7, 8, 9, 10 and 11, to break the sales data at the country level, with sales quantity, consumption value, and market share for key countries in the world, from 2021 to 2026.and Ultra-thin Six-Dimensional Force Sensor market forecast, by regions, by Type, and by Application, with sales and revenue, from 2027 to 2032.
Chapter 12, market dynamics, drivers, restraints, trends, and Porters Five Forces analysis.
Chapter 13, the key raw materials and key suppliers, and industry chain of Ultra-thin Six-Dimensional Force Sensor.
Chapter 14 and 15, to describe Ultra-thin Six-Dimensional Force Sensor sales channel, distributors, customers, research findings and conclusion.