1. Overview
Motion in a mechanical system is defined not only by the path an object follows, but also by how fast it moves, how its speed changes, where it stops, and how accurately it follows the commanded position.
Classification by motion trajectory focuses on spatial paths such as linear, rotational, arc, and curved motion. Classification by speed and position characteristics focuses on questions such as:
Is the speed maintained at a constant level?
Does the speed change in steps or continuously?
How are acceleration and deceleration performed?
Is only the target position important, regardless of the travel path?
Must the entire path be followed accurately during movement?
Is the position defined using an absolute or relative reference?
How much time is required for the position to stabilize after stopping?
How large is the difference between the commanded position and the actual position?
How much variation occurs when repeatedly moving to the same position?
Must the system follow the position of an external object or another axis?
Even when the same linear transfer mechanism is used, a constant-speed conveyor, point-to-point positioning axis, continuous-path machining axis, and tracking axis require different drive systems and control structures.
Speed and position characteristics are therefore fundamental design factors that determine:
Motor capacity
Gear reducer selection
Position sensor and encoder selection
Controller performance
Positioning accuracy
Repeatability
Cycle time
Product quality
Vibration and impact
Mechanical rigidity
Emergency-stop performance
2. Difference Between Motion Trajectory, Time Characteristics, and Speed and Position Characteristics
2.1 Motion Trajectory
Motion trajectory refers to the path followed by an object through space.
Typical examples include:
Linear path
Arc path
Circular path
Helical path
Curved path
Three-dimensional spatial path
2.2 Time Characteristics
Time characteristics describe when motion starts, how long it continues, and how often it repeats.
Typical examples include:
Continuous motion
Intermittent motion
Periodic motion
Event-driven motion
Synchronous motion
Intermittent-duty motion
2.3 Speed Characteristics
Speed characteristics describe how the velocity of an object changes according to time or position.
Typical examples include:
Constant-speed motion
Variable-speed motion
Accelerating motion
Decelerating motion
Low-speed approach motion
High-speed transfer motion
Step-speed motion
Speed-following motion
2.4 Position Characteristics
Position characteristics describe how the target position is defined and controlled.
Typical examples include:
Point-to-point positioning
Continuous-path control
Absolute-position movement
Relative-position movement
Index positioning
Multi-position positioning
Position-following motion
Homing
Position holding
A single motion may have all of these characteristics simultaneously.
For example, a ball-screw transfer axis driven by a servo motor can be described as follows:
Trajectory characteristic: Linear motion
Time characteristic: Intermittent motion
Speed characteristic: Trapezoidal or S-curve velocity profile
Position characteristic: Absolute point-to-point positioning
3. Basic Classification System for Speed and Position Characteristics
Speed and position characteristics can be analyzed according to the following criteria.
3.1 Classification by Speed-Maintenance Method
Constant-speed motion
Variable-speed motion
Step-speed motion
Low-speed motion
High-speed motion
Creep motion
3.2 Classification by Speed-Change Method
Constant-acceleration motion
Constant-deceleration motion
Accelerating and decelerating motion
Trapezoidal-velocity motion
Triangular-velocity motion
S-curve velocity motion
Emergency-stop motion
3.3 Classification by Speed Relationship
Independent-speed motion
Speed-synchronized motion
Ratio-speed motion
Speed-following motion
Master-slave motion
3.4 Classification by Position-Command Method
Absolute-position movement
Relative-position movement
Incremental-position movement
Home-referenced movement
Taught-position movement
3.5 Classification by Positioning Method
Point-to-point positioning
Multi-position positioning
Index positioning
Continuous-path position control
Position-following motion
Position-holding motion
3.6 Classification by Control-Accuracy Characteristics
Open-loop position control
Closed-loop position control
Single-feedback control
Dual-feedback control
Direct-position-detection control
4. Basic Concepts of Speed
4.1 Linear Velocity
Linear velocity is the change in position per unit time.
v = dx / dt
The symbols represent:
v: Linear velocity
x: Position or travel distance
t: Time
dx / dt: Rate of change in position with respect to time
Average velocity can be calculated as follows:
v_avg = Travel distance / Travel time
For example, when an object moves 500 mm in 2 seconds:
v_avg = 500 mm / 2 s = 250 mm/s
4.2 Rotational Speed
In rotational motion, angular velocity or revolutions per minute are used.
ω = dθ / dt
The symbols represent:
ω: Angular velocity
θ: Rotational angle
t: Time
Rotational speed is commonly expressed in revolutions per minute, or rpm.
4.3 Relationship Between Linear and Rotational Speed
The linear speed at the outer point of a rotating body can be calculated from the radius and angular velocity.
v = r × ω
The symbols represent:
v: Linear velocity
r: Rotational radius
ω: Angular velocity
Even at the same rotational speed, the linear speed increases as the radius increases.
5. Constant-Speed Motion
5.1 Definition
Constant-speed motion is motion in which the velocity of an object remains constant.
In ideal constant-speed motion, acceleration is zero.
a = 0
5.2 Main Characteristics
Product-transfer speed remains constant.
Process time is easy to predict.
Impact caused by speed variation is relatively small.
It is suitable for continuous processes.
Speed deviation may occur when the load changes.
5.3 Typical Applications
Belt conveyors
Roller conveyors
Continuous cutting devices
Constant-speed agitators
Pumps
Screw feeders
Film-feeding systems
Continuous production lines
5.4 Design Considerations
Target speed
Speed deviation
Load variation
Motor slip
Gear reducer efficiency
Speed sensor
Long-term speed stability
Product slipping
In constant-speed operation, even when the motor speed is constant, the actual product speed may differ because of belt slip or slipping between the product and the belt.
6. Variable-Speed Motion
6.1 Definition
Variable-speed motion is motion in which the operating speed changes according to process conditions or control commands.
Speed may change in steps or continuously.
6.2 Main Characteristics
Speed can be adjusted according to production conditions.
Operating speed can be changed for different product types.
Different speeds can be applied to different process sections.
Acceleration and deceleration conditions are required when speed changes.
The response performance of the speed controller is important.
6.3 Typical Applications
Inverter-driven conveyors
Servo transfer axes
Variable-speed mixers
Variable-flow pumps
Product-specific speed-change systems
Cutting machines with process-dependent speed changes
6.4 Design Considerations
Minimum speed
Maximum speed
Speed-control range
Low-speed torque
Speed-change time
Speed stability
Motor cooling
Allowable reducer speed
7. Step-Speed Motion
7.1 Definition
Step-speed motion selects one of several preset speeds for operation.
The speed does not vary continuously but changes between predefined levels.
7.2 Typical Speed Levels
Low speed
Medium speed
High speed
Approach speed
Working speed
Return speed
7.3 Main Characteristics
Control is relatively simple.
Process-specific speed settings are easy to configure.
Settings are easier to manage than with continuously variable speed.
Impact may occur during speed transitions.
Acceleration and deceleration periods are required between speed levels.
7.4 Typical Applications
High-speed approach followed by low-speed processing
Low-speed inspection followed by high-speed return
Two-speed or three-speed conveyors
High-speed and low-speed switching of pneumatic cylinders
Approach, machining, and return motion in drilling equipment
8. Low-Speed Motion
8.1 Definition
Low-speed motion is movement performed at a low speed to achieve precise positioning, stable contact, or safe operation.
8.2 Main Characteristics
Position error can be reduced more easily.
Impact and vibration are small.
Safety can be improved in areas close to operators.
Friction and stick-slip may affect performance.
Low-speed motor torque and control resolution are important.
8.3 Typical Applications
Homing
Precision-position approach
Approach immediately before assembly
Mold alignment
Product contact
Movement to an inspection position
Maintenance jog operation
8.4 Design Considerations
Low-speed torque
Speed ripple
Stick-slip
Gear reducer backlash
Encoder resolution
Friction variation
Lubrication condition
9. Creep Motion
9.1 Definition
Creep motion is movement at a very low speed when approaching a target position or contact point.
It is used for more precise final positioning than ordinary low-speed motion.
9.2 Main Purposes
Preventing overshoot of the target position
Reducing collision impact
Improving home-sensor detection accuracy
Reducing contact force
Improving positioning repeatability
Enabling safe machine adjustment
9.3 Typical Applications
Final approach during homing
Immediately before mold closing
Immediately before clamp contact
Measuring-probe approach
Product-alignment approach
Precision robotic insertion
9.4 Design Considerations
Creep speed
Sensor response time
Braking distance
Friction
Position resolution
Stopping delay
Controller scan time
10. High-Speed Motion
10.1 Definition
High-speed motion is performed at a high velocity to reduce cycle time and increase productivity.
10.2 Main Characteristics
Travel time can be reduced.
Inertial force and vibration increase.
Braking distance increases.
Mechanical rigidity and natural frequency are important.
Sensor and controller response performance are important.
Repeated bending loads on cables and hoses increase.
10.3 Typical Applications
High-speed pick-and-place systems
Product-transfer systems in packaging machines
Sorting devices
High-speed cutters
Delta robots
High-speed linear-motor axes
Semiconductor equipment
10.4 Design Considerations
Maximum speed
Maximum acceleration
Braking distance
Frame rigidity
Allowable guide speed
Ball-screw critical speed
Belt vibration
Cable life
Emergency-stop performance
11. Accelerating Motion
11.1 Definition
Accelerating motion is motion in which velocity increases over time.
Acceleration is expressed as follows:
a = dv / dt
11.2 Main Characteristics
Inertial force is generated as speed changes.
Additional motor torque is required.
Shorter acceleration time requires greater torque.
Product slipping or oscillation may occur.
11.3 Required Acceleration Force
The force required for acceleration can be calculated as follows:
F = m × a
The symbols represent:
F: Acceleration force
m: Moving mass
a: Acceleration
For a rotating axis, the required acceleration torque can be expressed as follows:
T = J × α
The symbols represent:
T: Acceleration torque
J: Moment of inertia
α: Angular acceleration
11.4 Design Considerations
Moving mass
Load inertia
Acceleration time
Maximum torque
Motor current
Product slipping
Structural deformation
Vibration
12. Decelerating Motion
12.1 Definition
Decelerating motion reduces the speed of a moving object.
It is used for stopping at a target position, reversing direction, or performing a safe stop.
12.2 Main Characteristics
Braking force is required during deceleration.
Inertial energy is transferred to the motor or brake.
Rapid deceleration increases impact and vibration.
It affects stopping error and overshoot.
12.3 Typical Applications
Approaching a target position
Conveyor stopping
Robot stopping
Rotational-axis deceleration
Emergency stopping
Indexing-table stopping
12.4 Design Considerations
Deceleration
Braking distance
Regenerative energy
Braking resistor
Mechanical brake
Product slipping
Stopping-position error
Structural impact
13. Trapezoidal-Velocity Motion
13.1 Definition
Trapezoidal-velocity motion consists of acceleration, constant velocity, and deceleration.
It is called a trapezoidal-velocity profile because the velocity-time graph forms a trapezoidal shape.
13.2 Motion Periods
Acceleration period
Constant-velocity period
Deceleration period
13.3 Main Characteristics
It is relatively simple to implement.
Travel time is easy to calculate.
It is widely used for servo-motor and stepper-motor positioning.
Acceleration may change suddenly.
Impact and vibration may occur in high-speed equipment.
13.4 Typical Applications
Ball-screw positioning axes
Belt-driven transfer axes
XY tables
Automatic assembly machines
CNC feed axes
Pick-and-place devices
14. Triangular-Velocity Motion
14.1 Definition
Triangular-velocity motion occurs when the travel distance is too short to reach a constant-velocity period, causing the motion to change directly from acceleration to deceleration.
14.2 Main Characteristics
It occurs over short travel distances.
There is no constant-velocity period.
Acceleration performance is more important than maximum speed.
It is suitable for repeated short-stroke operation.
14.3 Typical Applications
Short-distance pick-and-place systems
Small pushers
Short-stroke sealing devices
High-speed sorting devices
Small servo actuators
15. S-Curve Velocity Motion
15.1 Definition
S-curve velocity motion smoothly increases and decreases speed by limiting jerk, which is the rate of change in acceleration.
Jerk is expressed as follows:
j = da / dt
The symbols represent:
j: Jerk
a: Acceleration
t: Time
15.2 Main Characteristics
Impact is reduced.
Vibration is reduced.
Product movement can be minimized.
Mechanical fatigue can be reduced.
It is suitable for precision positioning.
Control is more complex than with a trapezoidal profile.
15.3 Typical Applications
Transfer of liquid containers
Food-tray transfer
Semiconductor equipment
Precision-assembly equipment
High-speed robots
Large transfer axes
Transfer of glass and brittle materials
16. Emergency-Stop Motion
16.1 Definition
Emergency-stop motion reduces speed to zero in a shorter time than normal deceleration.
It is used during emergency stops, collision avoidance, or hazard detection.
16.2 Main Characteristics
Very large deceleration forces occur.
Impact may be applied to the structure and product.
Large loads act on the brake and motor.
Safety takes priority over stopping-position accuracy.
16.3 Design Considerations
Emergency-stop distance
Maximum deceleration
Brake torque
Regenerative energy
Mechanical rigidity
Product displacement
Axis-to-axis collision
Braking method during power failure
17. Independent-Speed Motion
17.1 Definition
Independent-speed motion is a method in which each axis or device operates independently without maintaining a direct speed relationship with another axis.
17.2 Typical Applications
Independent conveyors
Individual pumps
Independent fans
Multiple independent workstations
Production lines with buffers
17.3 Main Characteristics
The control structure is simple.
The speed of each device can be adjusted independently.
Speed imbalance may occur between devices.
Buffers may be required to prevent product accumulation.
18. Speed-Synchronized Motion
18.1 Definition
Speed-synchronized motion is motion in which two or more axes move at the same speed or at a constant speed ratio.
18.2 Main Characteristics
The speed relationship between axes is maintained.
Product speed can be matched with the speed of a processing device.
If speed error accumulates, a position difference may occur.
Encoder feedback is important.
18.3 Typical Applications
Dual-drive conveyors
Packaging-film feed axes
Printing rollers
Synchronous belt axes
Multiple rollers
Electronic-gearing systems
18.4 Speed Ratio
The speed relationship between the master axis and slave axis can be expressed as follows:
v_slave = R × v_master
The symbols represent:
v_slave: Slave-axis speed
v_master: Master-axis speed
R: Speed ratio
19. Speed-Following Motion
19.1 Definition
Speed-following motion measures the speed of another axis or moving object in real time and follows it at the same or proportional speed.
19.2 Typical Applications
Conveyor-tracking robots
Flying cutters
Labeling during movement
Inspection of moving products
Continuous packaging systems
Web-tension control
19.3 Main Characteristics
Real-time speed measurement is required.
Communication and control delay are important.
The system must respond quickly to speed changes.
Tracking error may accumulate into position error.
19.4 Speed Error
Speed error can be expressed as follows:
e_v = v_cmd - v_act
The symbols represent:
e_v: Speed error
v_cmd: Commanded speed
v_act: Actual speed
20. Absolute-Position Movement
20.1 Definition
Absolute-position movement moves to a target coordinate measured from a fixed reference point.
The target position is specified as an absolute coordinate regardless of the current position.
20.2 Example
Assume that the current position is 100 mm and the following command is given:
Target position = 500 mm
In absolute-position movement, the axis moves to the 500 mm position.
The actual travel distance is:
Travel distance = 500 mm - 100 mm = 400 mm
20.3 Main Characteristics
Programs are easy to understand.
Multiple process positions are easy to manage.
A clear reference origin is required.
Position information may become incorrect if the origin is lost.
20.4 Typical Applications
CNC equipment
Robots
Multi-positioning systems
Automatic assembly machines
Servo indexing systems
21. Relative-Position Movement
21.1 Definition
Relative-position movement moves by a specified distance from the current position.
It is also called incremental-position movement.
21.2 Example
When the current position is 100 mm and the relative movement command is +500 mm:
Final position = 100 mm + 500 mm = 600 mm
21.3 Main Characteristics
It is suitable for repeated movement over the same distance.
The current position becomes the movement reference.
Repeated errors may accumulate.
It is suitable for pitch feeding.
21.4 Typical Applications
Product pitch feeding
Fixed-length cutting
Repeated step movement
Conveyor indexing
Metered rotation of screw feeders
22. Home-Referenced Movement
22.1 Definition
Home-referenced movement detects a machine reference position and establishes all position coordinates from that reference.
The home position becomes the basis of position control.
22.2 Homing Sequence
A typical homing sequence is performed as follows:
Move toward the home sensor at high speed.
Detect the home sensor.
Move away in the opposite direction.
Reapproach at low speed or creep speed.
Confirm the encoder index or sensor position.
Set the current coordinate as the reference position.
22.3 Main Characteristics
The position coordinate system is initialized.
It is often performed after power is turned on.
Repeatability is important.
Sensor hysteresis and approach speed affect accuracy.
22.4 Design Considerations
Type of home sensor
Approach direction
Approach speed
Sensor repeatability
Use of encoder Z-phase
Home offset
Mechanical stopper
23. Point-to-Point Positioning
23.1 Definition
Point-to-point positioning is a position-control method in which the start and target positions are important, while the intermediate travel path is relatively unimportant.
It is also called Point-to-Point Motion or PTP Motion.
23.2 Main Characteristics
Reaching the target position is the primary objective.
Path error during movement is relatively unimportant.
The position can be changed in the shortest possible time.
It is widely used in automation equipment.
23.3 Typical Applications
Pick-and-place systems
Product transfer
Automatic assembly machines
Indexing tables
Servo axes replacing pneumatic cylinders
Tool-changing devices
23.4 Design Considerations
Target position
Travel time
Acceleration and deceleration conditions
Position overshoot
Settling time
Repeatability
Position-holding torque
24. Multi-Position Positioning
24.1 Definition
Multi-position positioning moves one axis or device sequentially to several preset positions.
24.2 Typical Positions
Standby position
Product-loading position
Working position
Inspection position
Discharge position
Cleaning position
Maintenance position
24.3 Main Characteristics
Position data can be managed in a table.
Position settings can be changed according to product type.
Speed and acceleration can be set differently for each position.
The movement sequence between positions is important.
24.4 Typical Applications
Multi-level lifting systems
Robot positioners
Automated storage systems
Multi-process assembly machines
Multi-position filling systems
Multi-stage cutting devices
25. Index Positioning
25.1 Definition
Index positioning moves by a fixed distance or angle and stops accurately at the target position.
25.2 Main Characteristics
Fixed-pitch movement is repeated.
Movement and stopping are repeated.
Stopping-position repeatability is important.
It can be implemented with a mechanical indexer or servo axis.
25.3 Typical Applications
Rotary indexing tables
Turrets
Product pitch feeding
Packaging-film feeding
Automatic assembly machines
Multi-process machining equipment
25.4 Design Considerations
Index distance
Index angle
Dwell time
Position repeatability
Maximum allowable inertia
Dwell rigidity
Mechanical locking
26. Continuous-Path Position Control
26.1 Definition
Continuous-path position control continuously controls the complete path during movement, not only the starting and ending points.
It is also called Continuous Path Motion or CP Motion.
26.2 Main Characteristics
Path accuracy during movement is important.
Multiple axes are interpolated simultaneously.
Position and speed must be controlled together.
Speed must be adjusted according to curvature.
Controller processing performance is important.
26.3 Typical Applications
CNC machining
Robotic welding
Laser cutting
Painting robots
Adhesive dispensing
Contour machining
Cutting of complex shapes
26.4 Typical Interpolation Methods
Linear interpolation
Circular interpolation
Helical interpolation
Spline interpolation
Multi-axis interpolation
26.5 Design Considerations
Path error
Interpolation cycle
Axis synchronization
Corner deceleration
Radius of curvature
Following error
Controller processing speed
27. Position-Following Motion
27.1 Definition
Position-following motion tracks the position of another axis, moving object, or external reference in real time.
27.2 Typical Applications
Conveyor-tracking robots
Flying cutters
Packaging of moving products
Electronic cams
Web-tension control
Master-slave position control
27.3 Main Characteristics
Real-time position input is required.
Tracking delay may occur.
The difference between commanded and actual position is important.
Communication delay and control cycle affect performance.
27.4 Position Error
Position error can be expressed as follows:
e_p = x_cmd - x_act
The symbols represent:
e_p: Position error
x_cmd: Commanded position
x_act: Actual position
In position-following systems, an alarm or stop may be required when the position error exceeds a specified limit.
28. Position-Holding Motion
28.1 Definition
Position-holding motion maintains the target position after arrival so that external force or gravity does not cause displacement.
28.2 Typical Applications
Vertical lifting axes
Clamping axes
Robot joints
Press-position holding
Indexing tables
Height-adjustment systems
28.3 Position-Holding Methods
Motor holding torque
Servo position control
Electromagnetic brake
Mechanical brake
Worm gearbox
Clamping device
Mechanical locking pin
28.4 Design Considerations
External load
Gravitational load
Holding torque
Motor heat generation
Position holding during power failure
Brake life
Microvibration
Position drift
29. Open-Loop Position Control
29.1 Definition
Open-loop position control determines position from the input command and drive amount without directly measuring and correcting the actual position.
29.2 Typical Systems
Stepper motors
Pulse motors
Simple pneumatic cylinders
Mechanical stoppers
Cam-positioning systems
29.3 Main Characteristics
The structure is simple.
Cost is relatively low.
Actual position error cannot be detected directly.
Position error accumulates if step loss or slip occurs.
The system may be sensitive to load changes.
29.4 Suitable Conditions
Load variation is small.
Position-accuracy requirements are not high.
A mechanical stopper is present.
Low cost is important.
Movement speed and acceleration are low.
30. Closed-Loop Position Control
30.1 Definition
Closed-loop position control measures actual position using an encoder, linear scale, or position sensor and corrects the error between the commanded and actual positions.
30.2 Main Characteristics
Position error is corrected in real time.
High positioning accuracy can be achieved.
The system can respond to load changes.
Controller and sensor configuration are more complex.
Tuning is required.
30.3 Typical Systems
AC servo motors
Closed-loop stepper motors
Linear motors
Hydraulic servo systems
Robot joints
CNC feed axes
30.4 Design Considerations
Encoder resolution
Control gain
Following error
Overshoot
Settling time
Resonance
Sensor noise
Control cycle
31. Semi-Closed-Loop and Fully Closed-Loop Control
31.1 Semi-Closed-Loop Control
Semi-closed-loop control detects the motor-shaft position using a motor encoder.
The motor position can be controlled accurately, but ball-screw lead error, backlash, coupling deformation, and structural deformation cannot be detected directly.
31.2 Fully Closed-Loop Control
Fully closed-loop control directly measures the position of the actual moving table or workpiece using a linear scale.
31.3 Comparison
Item | Semi-Closed Loop | Fully Closed Loop |
|---|---|---|
Position-detection location | Motor shaft | Actual moving body |
Structure | Relatively simple | Complex |
Cost | Relatively low | High |
Backlash compensation | Limited | Possible |
Direct detection of ball-screw error | Not possible | Possible |
Typical applications | General servo axes | High-precision CNC and precision equipment |
32. Position Resolution
32.1 Definition
Position resolution is the smallest movement unit that the system can distinguish or command.
32.2 Resolution of a Screw-Driven Axis
The movement per pulse can be calculated using the screw lead and the number of command pulses per motor revolution.
Movement per pulse = Screw lead / Pulses per revolution
For example, when the screw lead is 10 mm and the command resolution is 10,000 pulses per revolution:
Movement per pulse = 10 mm / 10,000 = 0.001 mm
Therefore, the theoretical command resolution is 1 μm.
32.3 Factors Affecting Actual Resolution
Encoder resolution
Electronic gear ratio
Screw lead
Reduction ratio
Backlash
Friction
Structural deformation
Sensor noise
High theoretical command resolution does not necessarily produce the same level of actual positioning accuracy.
33. Positioning Accuracy
33.1 Definition
Positioning accuracy is the difference between the commanded target position and the actual reached position.
Position error can be expressed as follows:
e_p = x_cmd - x_act
33.2 Factors Affecting Positioning Accuracy
Ball-screw lead error
Gear reducer error
Backlash
Thermal expansion
Structural deformation
Encoder error
Controller compensation
Load variation
Assembly error
33.3 Methods for Improving Positioning Accuracy
Using a linear scale
Backlash compensation
Lead-error compensation
Temperature compensation
Improving mechanical rigidity
Using a precision reducer
Servo tuning
Precision assembly
34. Repeatability
34.1 Definition
Repeatability is the variation in reached position when repeatedly moving to the same target under the same conditions.
Positioning accuracy and repeatability are different concepts.
34.2 Difference Between Accuracy and Repeatability
Even when positioning accuracy is low, repeatability can be high if the system repeatedly reaches the same offset position.
For example, when the target position is 100 mm but the system always stops at 100.2 mm:
Positioning accuracy: Low
Repeatability: High
34.3 Factors Affecting Repeatability
Sensor repeatability
Backlash
Friction variation
Load variation
Approach direction
Temperature variation
Servo settling
Mechanical clearance
35. Backlash
35.1 Definition
Backlash is the phenomenon in which input motion is not transmitted immediately to the output because of mechanical clearance when the direction of motion reverses.
35.2 Typical Sources of Backlash
Gears
Gear reducers
Ball-screw nuts
Rack and pinion
Chains
Couplings
Linkage joints
35.3 Main Effects
Position error during direction reversal
Reduced repeatability
Vibration and impact
Path error
Servo instability
35.4 Methods for Reducing Backlash
Preloaded ball screw
Precision gear reducer
Dual pinion
Backlash compensation
Single-direction approach
Mechanical preload
Direct drive
36. Overshoot and Undershoot
36.1 Overshoot
Overshoot occurs when the moving body passes beyond the target position and then returns to it.
36.2 Undershoot
Undershoot occurs when the moving body fails to reach the target position or passes below the target during the correction process.
36.3 Causes
Excessive control gain
Low structural rigidity
High inertia
Insufficient damping
Backlash
Sensor delay
Rapid deceleration
36.4 Reduction Methods
Adjusting servo gain
Using an S-curve profile
Increasing deceleration time
Improving structural rigidity
Applying a vibration filter
Using feedforward control
Improving the load-inertia ratio
37. Settling Time
37.1 Definition
Settling time is the time required for the moving body to stabilize within the allowable position-error range after reaching the target position.
37.2 Main Effect
When settling time is long, the total cycle time increases even when the actual travel time is short.
The total positioning time can be expressed as follows:
T_positioning = t_move + t_settle
The symbols represent:
T_positioning: Total positioning time
t_move: Travel time
t_settle: Settling time
37.3 Factors Affecting Settling Time
Structural rigidity
Load inertia
Servo gain
Acceleration and deceleration conditions
Residual vibration
Damping
Backlash
Frame vibration
38. Following Error
38.1 Definition
Following error is the difference between the commanded position and actual position during movement.
Unlike static positioning error, it is a dynamic error that occurs while the axis is moving.
e_follow = x_cmd - x_act
38.2 Conditions That Increase Following Error
High speed
High acceleration
Insufficient motor torque
Large load inertia
Low control gain
Communication delay
Structural deformation
Friction variation
38.3 Main Effects
Path error
Synchronization error
Reduced machining quality
Cutting-position error
Packaging-position mismatch
Reduced robot-tracking performance
39. Comparison of Typical Applications by Speed and Position Characteristic
Classification | Main Characteristics | Typical Equipment | Key Design Factor |
|---|---|---|---|
Constant-speed motion | Maintains a constant speed | Conveyor, pump | Speed stability |
Variable-speed motion | Speed changes during operation | Inverter, servo axis | Speed range |
Step-speed motion | Switches between preset speed levels | Approach, work, and return axis | Transition impact |
Low-speed motion | Precise movement at low speed | Jogging, precision approach | Low-speed torque |
Creep motion | Final approach at very low speed | Homing, contact positioning | Sensor response |
High-speed motion | Long-distance movement in a short time | High-speed robot, transfer axis | Inertia, vibration |
Speed-synchronized motion | Maintains a speed relationship between axes | Rollers, film-feed axis | Speed ratio |
Speed-following motion | Follows another axis in real time | Flying cutter | Following error |
Absolute-position movement | Moves to a fixed coordinate | CNC, robot | Home reference |
Relative-position movement | Moves a specified distance from the current position | Pitch feeding | Accumulated error |
Point-to-point positioning | Start and target positions are important | Pick-and-place system | Settling time |
Continuous-path control | The entire path is important | CNC, welding robot | Path error |
Index positioning | Moves by a fixed distance or angle | Indexing table | Repeatability |
Position-following motion | Follows an external position in real time | Conveyor-tracking robot | Position delay |
Position-holding motion | Continuously holds a target position | Lifting axis, clamp | Holding torque |
Open-loop control | Controls without position feedback | Stepper motor | Step loss |
Closed-loop control | Corrects using actual position feedback | Servo motor | Encoder and tuning |
40. Criteria for Selecting Speed and Position Characteristics
40.1 Process Conditions
Is the process continuous?
Is work performed while the object is stationary?
Is processing required during movement?
Is only the target position important?
Is the complete travel path important?
Must product speed be synchronized with another device?
40.2 Speed Conditions
Minimum speed
Maximum speed
Constant-speed operation
Variable-speed range
Acceleration time
Deceleration time
Creep speed
Emergency-stop condition
40.3 Position Conditions
Target position
Travel distance
Number of positions
Absolute or relative position
Home reference
Position-holding time
Approach direction
40.4 Accuracy Conditions
Positioning accuracy
Repeatability
Position resolution
Speed accuracy
Path accuracy
Following error
Settling time
40.5 Load Conditions
Moving mass
Rotational inertia
Eccentric load
Vertical load
Friction
External force
Impact load
40.6 Mechanical-Structure Conditions
Frame rigidity
Guide rigidity
Ball-screw lead
Gear reducer backlash
Coupling rigidity
Thermal deformation
Vibration characteristics
40.7 Control Conditions
Open-loop or closed-loop control
Encoder resolution
Position sensor
Control cycle
Network delay
Interpolation function
Electronic cam
Homing function
41. Design Verification Items
41.1 Speed Verification
Ability to reach the target speed
Minimum-speed stability
Allowability of maximum speed
Speed fluctuation
Speed deviation under load variation
Acceleration and deceleration time
41.2 Position Verification
Positioning accuracy
Repeatability
Absolute-position error
Relative-movement error
Homing repeatability
Position-holding performance
41.3 Dynamic-Performance Verification
Following error
Overshoot
Settling time
Direction-reversal error
Residual vibration
Emergency-stop performance
41.4 Mechanical-Structure Verification
Backlash
Structural deformation
Ball-screw critical speed
Shaft torsion
Allowable guide speed
Bearing life
Gear reducer rigidity
41.5 Control-Performance Verification
Encoder resolution
Control cycle
Servo gain
Communication delay
Interpolation performance
Position-feedback abnormality
Sensor noise
41.6 Safety Verification
Emergency-stop distance
Position holding during power failure
Vertical-axis fall prevention
Speed limitation
Safe position
Collision prevention
Software limits
Hardware limits
42. Main Speed- and Position-Related Equations
Linear Velocity
v = dx / dt
Linear velocity is the rate of change in position with respect to time.
Average Velocity
v_avg = Travel distance / Travel time
Average velocity is the total travel distance divided by the travel time.
Angular Velocity
ω = dθ / dt
Angular velocity is the rate of change in rotational angle with respect to time.
Linear and Angular Velocity
v = r × ω
Linear velocity is the product of rotational radius and angular velocity.
Acceleration
a = dv / dt
Acceleration is the rate of change in velocity with respect to time.
Acceleration Force
F = m × a
Acceleration force is the product of moving mass and acceleration.
Acceleration Torque
T = J × α
Acceleration torque is the product of moment of inertia and angular acceleration.
Speed Error
e_v = v_cmd - v_act
Speed error is the difference between commanded speed and actual speed.
Position Error
e_p = x_cmd - x_act
Position error is the difference between commanded position and actual position.
Total Positioning Time
T_positioning = t_move + t_settle
Total positioning time is the sum of travel time and settling time.
Movement per Pulse
Movement per pulse = Screw lead / Pulses per revolution
Movement per pulse represents the theoretical minimum position-command unit.
Screw Travel Distance
x = n × L
The symbols represent:
x: Axial travel distance
n: Number of revolutions
L: Screw lead
43. Conclusion
Classification of motion according to speed and position characteristics is not simply a distinction between fast and slow movement.
Speed characteristics describe how velocity is maintained and changed during motion. Position characteristics describe how the target position is defined and how the actual position is controlled.
Constant-speed motion is suitable for continuous production flow, while variable-speed motion allows flexible response to changes in products and process conditions. Low-speed and creep motion are suitable for precise approach and safe contact. High-speed motion improves productivity, but inertia, vibration, and braking performance must also be evaluated.
Point-to-point positioning is suitable for automation equipment where reaching the target position is important. Continuous-path control is suitable for systems such as CNC machining, welding, and cutting, where accuracy along the entire path is important.
Absolute-position movement makes it easy to manage positions within a global coordinate system. Relative-position movement is suitable for systems that repeatedly move by a fixed pitch or distance. Position-following and speed-synchronized motion are important in high-speed automation systems that must maintain a precise relationship with another axis or moving product.
Positioning accuracy, repeatability, resolution, backlash, following error, overshoot, and settling time are different concepts. They must be evaluated separately to assess the actual performance of a machine correctly.
Motion design according to speed and position characteristics should therefore consider the following factors together:
Minimum and maximum speed
Constant-speed and variable-speed conditions
Acceleration and deceleration
Jerk
Target position
Absolute and relative coordinates
Positioning accuracy
Repeatability
Position resolution
Backlash
Following error
Overshoot
Settling time
Encoders and position sensors
Open-loop and closed-loop control
Emergency-stop distance
Position holding during power failure
Good motion design does not merely create a system that reaches a target position. It ensures stable movement at the required speed, accurate maintenance of path and speed during travel, stopping at the target without excessive overshoot or vibration, and repeatable operation under the same conditions.
Speed and position characteristics are fundamental motion-design criteria that determine productivity, precision, stability, safety, and equipment life.