1. Overview

In a mechanical system, Mechanism and Motion are not separate concepts.

Motion is the phenomenon in which the position or orientation of a component or working element changes over time. A Mechanism is a mechanical structure that converts and transmits an input force or motion into an output motion according to a defined relationship.

In other words, Motion is the resulting movement observed in a machine, while a Mechanism is the structural means that creates and constrains that movement.

The basic connection structure of a machine can be expressed as follows:

Energy source → Actuator → Power transmission element → Mechanism → Output motion → Work

A more detailed expression is:

Energy supply → Force or torque generation → Motion transmission → Motion conversion → Motion constraint → Formation of output position, speed, and force → Process execution

For example, motor rotation alone cannot move a product in a straight line. The motor’s rotational motion must be converted into linear motion through a mechanism such as a ball screw, belt, or rack and pinion before a transfer function can be achieved.

A Mechanism can therefore be understood as a connection structure that organizes the basic motion produced by an actuator into the Motion required for a specific purpose.

2. Definition of Motion

Motion is the phenomenon in which the position or orientation of an object changes over time.

If the position of an object is represented by x, its rotational angle by θ, and time by t, linear velocity and angular velocity can be expressed as follows:

v = dx / dt

ω = dθ / dt

The symbols represent:

• v: Linear velocity

• x: Linear position

• ω: Angular velocity

• θ: Rotational angle

• t: Time

Motion includes more than the path of movement. It also includes the following characteristics:

• Motion trajectory

• Travel distance

• Rotational angle

• Velocity

• Acceleration

• Direction of movement

• Repetition period

• Stopping position

• Positioning accuracy

• Force acting during motion

• Synchronization relationship between motions

Therefore, even two motions following the same straight path may have completely different mechanical characteristics depending on speed, acceleration, repetition pattern, and positioning accuracy.

3. Definition of Mechanism

A Mechanism is a mechanical arrangement in which one or more rigid components, joints, guides, or contact elements are connected in a defined relationship to convert input motion into output motion.

The main functions of a Mechanism include:

• Motion transmission

• Change of motion direction

• Conversion of motion type

• Increase or reduction of travel distance

• Speed conversion

• Torque and force conversion

• Trajectory generation

• Limitation of motion range

• Synchronization of multiple axes

• Formation of stopping positions

• Mechanical locking

• Generation of repetitive motion

Typical Mechanisms include:

• Gear mechanisms

• Belt-and-pulley mechanisms

• Chain-and-sprocket mechanisms

• Ball-screw mechanisms

• Rack-and-pinion mechanisms

• Slider-crank mechanisms

• Four-bar linkages

• Cam-and-follower mechanisms

• Geneva mechanisms

• Toggle mechanisms

• Ratchet mechanisms

• Differential mechanisms

• Parallel linkages

• Robotic linkage mechanisms

4. Difference Between Machine, Mechanism, and Motion

Machine, Mechanism, and Motion are connected concepts, but they have different meanings.

4.1 Machine

A Machine is a complete system that uses energy to perform a specific task or process.

Examples include:

• Packaging machine

• Cutting machine

• Filling machine

• Press

• Conveyor

• Robot

• Meat-processing machine

4.2 Mechanism

A Mechanism is a mechanical structure within a Machine that transmits or converts motion.

For example, the following structures inside a packaging machine are Mechanisms:

• Film-feed rollers

• Sealing-bar lifting linkage

• Product pusher

• Cam indexer

• Cutting-blade drive mechanism

4.3 Motion

Motion is the actual movement that occurs in the components and output elements of a Mechanism.

Examples include:

• Roller rotation

• Linear reciprocation of a sealing bar

• Vertical movement of a cutting blade

• Forward and return motion of a product pusher

• Intermittent rotation of an indexing table

Their relationship can be summarized as follows:

A Machine performs a process.

A Mechanism creates the motion required for the process.

Motion is the actual movement generated by the Mechanism.

5. Basic Relationship Between Mechanism and Motion

The relationship between Mechanism and Motion can be organized into four main functions.

5.1 Motion Generation

An actuator supplies input motion to the Mechanism.

Examples:

• Motor rotation

• Linear movement of a cylinder

• Spring return

• Gravity-induced falling

5.2 Motion Transmission

Input motion is transmitted to an output element located elsewhere.

Examples:

• Shaft

• Gear

• Belt

• Chain

• Linkage

5.3 Motion Conversion

The type of input motion is converted into another type of motion.

Examples:

• Rotation → Linear motion

• Rotation → Reciprocating motion

• Rotation → Oscillating motion

• Linear motion → Rotation

• Continuous rotation → Intermittent rotation

5.4 Motion Constraint

The output component is constrained to move only in the required direction and along the required path.

Examples:

• Linear guide

• Rotary shaft and bearing

• Linkage joint

• Cam groove

• Curved rail

• Mechanical stopper

A Mechanism not only creates motion but also eliminates unnecessary movement so that only the required degrees of freedom remain.

6. Overall Connection Structure

The connection between Mechanism and Motion can be divided functionally as follows.

6.1 Energy Path

Energy source → Drive device → Power transmission section → Working section

Example:

Power supply → Servo drive → Servo motor → Reducer → Linkage → Gripper

6.2 Motion Path

Input motion → Transmitted motion → Converted motion → Output motion

Example:

Motor rotation → Reduced-speed rotation → Crank rotation → Linear reciprocation of a slider

6.3 Force-Transmission Path

Actuator force → Transmission component → Joint or guide → Output element → Workpiece

This path is called the load path.

6.4 Signal Path

Sensor → Controller → Drive or valve → Actuator

6.5 Feedback Path

Actual position, speed, or force → Sensor → Controller → Correction command → Actuator

The complete system can be expressed as follows:

Command → Controller → Actuator → Mechanism → Motion → Work

The output result then returns through the following path:

Motion → Sensor → Controller → Correction

7. Input Motion and Output Motion

A Mechanism generally has an input section and an output section.

7.1 Input Motion

Input motion is supplied to the Mechanism by an actuator or external force.

Typical input motions include:

• Continuous rotation

• Limited-angle rotation

• Linear movement

• Reciprocating movement

• Vibration

• Manual operation

• Gravity-induced falling

7.2 Output Motion

Output motion is the movement generated by the Mechanism in the form required for the actual work.

Typical output motions include:

• Linear transfer

• Rotational transfer

• Reciprocating motion

• Oscillating motion

• Intermittent rotation

• Compound trajectory

• Clamping motion

• Cutting motion

7.3 Input–Output Relationship

The core of mechanism design is defining the relationship between input and output motion.

Output position can generally be expressed as follows:

q_out = f(q_in)

The symbols represent:

• q_in: Input position or input angle

• q_out: Output position or output angle

• f: Conversion relationship determined by the geometry and dimensions of the Mechanism

For example, in a ball screw, the relationship between motor revolutions and travel distance is:

x = n × L

The symbols represent:

• x: Linear travel distance

• n: Number of screw revolutions

• L: Screw lead

8. Kinematic Chain

A kinematic chain is a structure in which multiple links are connected through joints.

The motion of the input link is transmitted sequentially to the other links.

8.1 Link

A link is a rigid component that transmits motion.

Examples:

• Lever

• Crank

• Connecting rod

• Slider

• Robot arm

• Cam

8.2 Joint

A joint is a connection between two links that permits specific relative motion while restricting other motion directions.

Typical joints include:

• Revolute joint

• Prismatic joint

• Screw joint

• Spherical joint

• Cylindrical joint

• Cam contact

• Gear contact

8.3 Fixed Link

When one link in a kinematic chain is fixed to the frame, the chain becomes an actual Mechanism.

In other words, a structure in which all links move freely is a kinematic chain. When one or more links are fixed to a reference structure and the input and output are defined, it becomes a Mechanism.

9. Degrees of Freedom and Motion Constraint

Degrees of freedom indicate the number of independent motion variables available to a Mechanism.

A free rigid body in three-dimensional space can have up to six degrees of freedom:

• Translation along the X-axis

• Translation along the Y-axis

• Translation along the Z-axis

• Rotation around the X-axis

• Rotation around the Y-axis

• Rotation around the Z-axis

A Mechanism removes unnecessary degrees of freedom through joints and guides.

For example, a linear guide constrains a moving body so that only translation in one direction is allowed.

A rotary shaft and bearing permit only rotation around the shaft axis.

The degree of freedom of a Mechanism can be conceptually expressed as:

Mechanism degree of freedom = Total possible motion - Motion eliminated by joints and constraints

If the degree of freedom is too low, the Mechanism may not move or may become overconstrained.

If the degree of freedom is too high, the output position may become unstable.

10. Role of Constraint and Guidance

In a Mechanism, motion guidance is as important as motion generation.

Even when an actuator generates force, the required Motion cannot be obtained unless the output component is properly guided.

10.1 Guidance for Linear Motion

• Linear guide

• Slide bushing

• V-guide

• Roller guide

• Prismatic guide

10.2 Guidance for Rotational Motion

• Ball bearing

• Roller bearing

• Bushing

• Pivot

• Turntable bearing

10.3 Guidance for Curved Motion

• Cam groove

• Curved rail

• Linkage-generated path

• Multi-axis robotic interpolation

The drive element generates motion, while the guide element determines the motion direction and trajectory.

A ball screw transmits axial force, but the moment load and lateral load of the moving table are generally supported by linear guides.

11. Relationship Between Actuator and Mechanism

The actuator and the Mechanism perform different roles.

11.1 Role of the Actuator

The actuator converts energy into mechanical force or torque.

Typical actuators include:

• Electric motor

• Servo motor

• Stepper motor

• Linear motor

• Pneumatic cylinder

• Hydraulic cylinder

• Solenoid

• Piezoelectric actuator

11.2 Role of the Mechanism

The Mechanism organizes the actuator output into the Motion required for the work.

Example:

Servo motor → Generates rotational torque

Ball screw → Converts rotation into linear movement

Linear guide → Constrains movement to a linear path

Table → Moves the product to the target position

Therefore, the actuator creates the energy of motion, while the Mechanism creates the form and relationship of motion.

12. Motion-Transmission Mechanisms

Motion-transmission mechanisms transfer input motion to an output element located at a distance.

12.1 Shaft Transmission

A rotating shaft transmits torque and rotational motion.

12.2 Gear Transmission

Meshing gears change speed, torque, and direction.

12.3 Belt Transmission

A belt and pulley transmit motion between separated shafts.

12.4 Chain Transmission

A chain and sprocket provide rotational transmission without slip.

12.5 Linkage Transmission

Links and joints transmit motion to another position.

12.6 Fluid Transmission

Pneumatic or hydraulic pressure transmits force to a remote actuator.

When selecting a transmission mechanism, distance, load, speed, accuracy, backlash, noise, and maintenance must be considered.

13. Motion-Conversion Mechanisms

A Mechanism converts input Motion into the required output Motion.

13.1 Rotation-to-Linear Conversion

Typical mechanisms:

• Ball screw

• Lead screw

• Rack and pinion

• Belt slider

• Cam and follower

13.2 Rotation-to-Reciprocating Conversion

Typical mechanisms:

• Slider-crank mechanism

• Eccentric cam

• Scotch-yoke mechanism

• Eccentric shaft

13.3 Rotation-to-Oscillating Conversion

Typical mechanisms:

• Crank-rocker mechanism

• Four-bar linkage

• Cam rocker

• Sector gear

13.4 Continuous Rotation-to-Intermittent Motion Conversion

Typical mechanisms:

• Geneva mechanism

• Cam indexer

• Ratchet and pawl

• Clutch and brake

13.5 Linear-to-Rotational Conversion

Typical mechanisms:

• Rack and pinion

• Lever

• Linkage

• Cable drum

14. How a Mechanism Determines Motion Trajectory

The geometry and connection conditions of a Mechanism determine the trajectory of the output element.

14.1 Trajectory Determined by a Guide

A linear guide or curved rail directly determines the path of the output element.

14.2 Trajectory Determined by Link Length

In a four-bar or multi-link mechanism, link length and joint position determine the trajectory of the output point.

14.3 Trajectory Determined by Cam Profile

In a cam mechanism, the shape of the cam surface determines follower displacement and the law of motion.

14.4 Trajectory Determined by Multi-Axis Control

In a robot or CNC machine, the output-point trajectory is generated by combining the motions of multiple axes.

Therefore, Motion trajectory is not determined only by the actuator’s direction of movement. It is determined by the geometric structure of the Mechanism.

15. Position Relationship

A geometric relationship exists between the input position and output position of a Mechanism.

A general position relationship can be expressed as:

x_out = f(x_in, geometry)

The relationship between rotational input and linear output can be expressed as:

x = f(θ)

The term geometry includes:

• Link length

• Rotational radius

• Gear pitch

• Screw lead

• Cam profile

• Joint position

• Guide direction

When the geometry of a Mechanism is fixed, the output position is mechanically determined by the input position.

16. Velocity Relationship

Output velocity can be obtained by differentiating the input–output position relationship with respect to time.

Assume that the input–output relationship is:

x = f(θ)

Output velocity can then be expressed as:

v = dx / dt

v = dx / dθ × dθ / dt

v = dx / dθ × ω

This relationship means that output velocity may vary according to the Mechanism position even when the input rotational speed is constant.

For example, in a slider-crank mechanism, the slider velocity is not constant even when the crank rotates at a constant speed.

Slider velocity becomes zero at both ends of the stroke and increases near the middle of the stroke.

17. Acceleration Relationship

Output acceleration is the rate of change in output velocity over time.

a = dv / dt

Even when input velocity is constant, output acceleration may continuously change if the geometric relationship of the Mechanism is nonlinear.

Changes in acceleration directly affect:

• Inertial force

• Motor torque

• Link load

• Bearing reaction force

• Impact

• Vibration

• Product oscillation

• Noise

• Fatigue life

Mechanism design must therefore evaluate not only output trajectory but also changes in velocity and acceleration.

18. Relationship Between Force and Torque

A Mechanism converts not only motion but also force and torque.

18.1 Lever

In a lever, the following force-distance relationship applies:

F_in × l_in = F_out × l_out

The symbols represent:

• F_in: Input force

• l_in: Distance from the pivot on the input side

• F_out: Output force

• l_out: Distance from the pivot on the output side

When the output-side distance becomes shorter, the output force increases, but the output travel decreases.

18.2 Reducer

In an ideal reducer, output torque increases as follows:

T_out = T_in × i × η

The symbols represent:

• T_out: Output torque

• T_in: Input torque

• i: Reduction ratio

• η: Efficiency

18.3 Screw Mechanism

A screw mechanism can convert relatively small rotational torque into a large axial force.

A smaller screw lead reduces travel per revolution but makes it easier to obtain a larger axial force.

In a Mechanism, an increase in force generally involves a trade-off with travel distance or speed.

19. Power Relationship

In an ideal Mechanism, input power and output power are equal.

P_in = P_out

Rotational power is expressed as:

P = T × ω

Linear power is expressed as:

P = F × v

Therefore, in an ideal rotary-to-linear conversion mechanism:

T × ω = F × v

In an actual Mechanism, losses occur because of friction and deformation:

P_out = P_in × η

The symbol η represents mechanism efficiency.

When a Mechanism increases force, output speed generally decreases. When it increases speed, output force generally decreases.

20. Direct Drive and Indirect Drive

20.1 Direct Drive

Direct drive transmits actuator output directly to the load.

Typical examples include:

• Linear motor

• Torque motor

• Direct-drive rotary table

• Motorized roller

Advantages:

• Low backlash

• High responsiveness

• Fewer components

• High transmission efficiency

Limitations:

• A larger actuator may be required.

• Load inertia directly affects the actuator.

• Thermal management is important.

• Actuator cost may be high.

20.2 Indirect Drive

Indirect drive transmits or converts motion through a reducer, belt, screw, linkage, or cam.

Advantages:

• Force and torque can be increased.

• Motor location can be arranged more freely.

• Various types of Motion can be generated.

• Large loads can be driven more easily.

Limitations:

• Backlash may occur.

• Transmission losses occur.

• The number of wear components increases.

• The structure becomes more complex.

21. Serial Mechanism Structure

A serial Mechanism is a structure in which multiple links and joints are connected sequentially.

Motion and load are transmitted from input to output through one continuous path.

Typical examples include:

• Articulated robot

• Crane boom

• Link-type transfer arm

• Multi-stage reducer

• Multi-stage gear train

Main Characteristics

• A large working range is easy to achieve.

• Complex orientations can be produced.

• Joint errors may accumulate at the output.

• Output rigidity may be relatively low.

• Output-end inertia may increase.

22. Parallel Mechanism Structure

A parallel Mechanism is a structure in which multiple links or actuators simultaneously support and drive a single output platform.

Typical examples include:

• Delta robot

• Stewart platform

• Parallel-link positioning system

• Three-point or four-point lifting system

Main Characteristics

• High rigidity can be achieved.

• Loads can be distributed through multiple paths.

• Moving mass can be reduced.

• It is suitable for high-speed operation.

• Kinematics and control are complex.

• Working range may be limited.

23. Closed-Loop Mechanical Structure

A closed-loop mechanical structure is a Mechanism in which links form one or more closed loops.

Typical examples include:

• Four-bar linkage

• Slider-crank mechanism

• Toggle mechanism

• Parallel linkage

• Parallel robot

In a closed-loop Mechanism, the positions of multiple links are mutually constrained.

Therefore, several components can move in a defined relationship using only one input.

However, inaccurate assembly tolerances or joint positions may cause overconstraint, jamming, or internal stress.

24. Mechanical Synchronization and Electronic Synchronization

24.1 Mechanical Synchronization

One drive source is distributed through gears, belts, chains, a camshaft, or a line shaft to synchronize multiple motions.

Advantages:

• Phase relationships are maintained mechanically.

• The control structure is simple.

• Repeatability is high.

Limitations:

• Motion changes are difficult.

• The structure may become long and complex.

• Mechanical backlash and wear occur.

• A fault in one section may affect the entire system.

24.2 Electronic Synchronization

Each axis uses an individual servo motor, and speed and position are synchronized by a controller.

Typical functions include:

• Electronic gearing

• Electronic cam

• Master-slave control

• Position interpolation

• Phase compensation

Advantages:

• Motion conditions can be changed by software.

• Product-specific setup changes are easy.

• Individual-axis compensation is possible.

• Mechanical transmission components can be reduced.

Limitations:

• The control system is complex.

• Encoder and communication performance are important.

• Communication delay and control-cycle time affect performance.

25. Connection Between Mechanism and Control System

In traditional Mechanisms, motion relationships were determined by mechanical geometry.

In modern automated equipment, Mechanisms and control systems work together to create Motion.

The basic structure is:

Motion command → Motion controller → Servo drive → Motor → Mechanism → Output Motion

25.1 Position Control

The difference between target position and actual position is corrected.

e_p = x_cmd - x_act

The symbols represent:

• e_p: Position error

• x_cmd: Commanded position

• x_act: Actual position

25.2 Speed Control

The difference between commanded speed and actual speed is corrected.

e_v = v_cmd - v_act

25.3 Force or Torque Control

The force applied to the workpiece or the axis torque is adjusted to a target value.

The Mechanism converts control commands into actual machine motion, but backlash, friction, rigidity, and inertia directly affect control performance.

26. Sensor and Feedback Structure

Sensors measure the actual Motion generated by the Mechanism.

26.1 Position Sensors

• Encoder

• Linear scale

• Potentiometer

• Resolver

• Proximity sensor

• Limit switch

26.2 Speed Sensors

• Speed calculation from encoder signals

• Tachogenerator

• Laser speed sensor

26.3 Force and Torque Sensors

• Load cell

• Torque sensor

• Pressure sensor

• Strain gauge

26.4 Condition Sensors

• Vibration sensor

• Temperature sensor

• Pressure switch

• Door sensor

• Product-detection sensor

The feedback structure can be expressed as:

Command → Actuator → Mechanism → Motion

Motion → Sensor → Controller → Correction command

27. Rigidity and Elastic Deformation

An actual Mechanism is not a perfectly rigid body.

Shafts, links, frames, belts, chains, and couplings deform under load.

Mechanism deformation can be conceptually expressed as:

δ = F / k

The symbols represent:

• δ: Deformation

• F: Applied force

• k: Mechanism rigidity

Low rigidity can cause:

• Position error

• Vibration

• Increased settling time

• Resonance

• Reduced machining quality

• Variation in clamping force

• Delay in output motion

In high-precision Motion systems, the rigidity of the entire Mechanism must be evaluated together with actuator resolution.

28. Backlash and Clearance

Backlash is the phenomenon in which input motion is not immediately transmitted to the output because of internal clearance when the motion direction reverses.

Typical sources include:

• Gear mesh

• Reducer

• Ball-screw nut

• Rack and pinion

• Chain

• Linkage joint

• Coupling

Backlash may cause:

• Position error during direction reversal

• Reduced repeatability

• Impact

• Noise

• Following error

• Servo instability

Methods for reducing backlash include:

• Preloading

• Precision reducer

• Dual pinion

• Preloaded ball screw

• Single-direction approach

• Software compensation

• Direct drive

29. Friction and Efficiency

Friction resists the motion of a Mechanism while generating energy loss and heat.

Friction affects:

• Required motor torque

• Low-speed stability

• Position repeatability

• Mechanism efficiency

• Heat generation

• Wear

• Service life

• Stick-slip

At low speed, stick-slip may occur because of the difference between static and kinetic friction.

Precision transfer axes must therefore consider the guide type, lubrication, seal resistance, and preload together.

30. Inertia and Motion Response

Each component of a Mechanism has mass and inertia.

In linear motion, mass affects the required acceleration force.

F = m × a

In rotational motion, moment of inertia affects the required acceleration torque.

T = J × α

The symbols represent:

• T: Acceleration torque

• J: Moment of inertia

• α: Angular acceleration

When a reducer is used, the output-side inertia is reflected to the motor side.

Large moving mass and rotational inertia cause:

• Increased motor capacity

• Longer acceleration time

• Increased braking distance

• Increased energy consumption

• Increased vibration

• Increased structural load

In a high-speed Mechanism, minimizing moving mass is especially important.

31. Mechanism Types and Typical Motion

32. Connection Example 1: Ball-Screw Transfer Axis

The connection structure of a ball-screw transfer axis is:

Servo drive → Servo motor → Coupling → Ball screw → Nut → Moving table

The separate guiding structure is:

Frame → Linear guide → Moving table

The feedback structure is:

Motor encoder or linear scale → Controller

Role of Each Element

• Servo motor: Generates rotational torque

• Coupling: Transmits rotation and absorbs alignment error

• Ball screw: Converts rotational motion into linear motion

• Linear guide: Forms the linear path and supports moment load

• Table: Moves the workpiece

• Encoder: Detects actual position

33. Connection Example 2: Slider-Crank Mechanism

The connection structure is:

Motor → Reducer → Crankshaft → Connecting rod → Slider → Working element

Motion Relationship

• Motor: Continuous rotation

• Reducer: Reduces rotational speed and increases torque

• Crank: Generates rotational radius

• Connecting rod: Transmits motion

• Slider: Produces linear reciprocating motion

• Working element: Performs cutting, pressing, or transfer

Main Characteristics

• Stroke is determined by crank radius.

• Slider velocity is not constant.

• Velocity becomes zero at both ends of the stroke.

• Inertial load increases during direction reversal.

34. Connection Example 3: Cam and Follower

The connection structure is:

Motor → Camshaft → Cam profile → Follower → Output link or slider

The cam shape determines:

• Output displacement

• Rise section

• Return section

• Dwell section

• Output velocity

• Output acceleration

A cam can mechanically generate complex repetitive Motion from one continuous rotational input.

However, changing the motion condition requires changing the cam profile.

35. Connection Example 4: Pneumatic-Cylinder Drive

The connection structure is:

Air compressor → Air tank → Valve → Pneumatic cylinder → Rod → Working element

The control path is:

Sensor → PLC → Solenoid valve → Cylinder

Role of Each Element

• Compressed air: Supplies energy

• Valve: Controls airflow direction and flow rate

• Cylinder: Converts pressure into linear force

• Guide: Supports lateral load on the rod

• Stopper or sensor: Determines position

A pneumatic cylinder directly generates linear Motion, but a separate guide and stopper are often required for precise guidance and repeatability.

36. Connection Example 5: Indexing Table

The connection structure of an indexing table can be configured as follows.

Mechanical Method

Motor → Reducer → Cam indexer → Rotary table

Servo Method

Servo motor → Precision reducer → Rotary table

A mechanical indexer creates movement and dwell through the cam profile.

A servo indexer allows the movement angle, speed, acceleration, and dwell time to be changed by software.

37. Connection Example 6: Articulated Robot

The connection structure of an articulated robot is:

Servo motor → Reducer → Joint → Link → Next joint → End effector

The rotational Motion of each joint is combined to determine the spatial position and orientation of the end effector.

If the joint coordinates are represented by q, the end-effector position can be expressed as:

X = f(q)

The symbols represent:

• q: Position of each joint

• X: Position and orientation of the end effector

• f: Kinematic relationship determined by the robot linkage structure

In a serial robot, joint errors and link deformation may accumulate at the end effector.

38. Process for Connecting Function to Motion

In machine design, the Mechanism should not be selected first.

The required function should first be converted into Motion requirements, and then an appropriate Mechanism should be selected.

The basic procedure is as follows.

38.1 Define the Function

Example:

Move a product to the next process position.

38.2 Define the Required Motion

• Linear movement

• Travel distance: 300 mm

• Travel time: 1 second

• Stopping repeatability: ±0.1 mm

• Repetition: 30 cycles per minute

38.3 Define the Load

• Product mass

• Moving-table mass

• Friction

• Acceleration

• External force

38.4 Select Actuator Candidates

• Pneumatic cylinder

• Servo motor

• Stepper motor

• Linear motor

38.5 Select Mechanism Candidates

• Ball screw

• Timing belt

• Rack and pinion

• Direct cylinder drive

38.6 Select the Guidance Structure

• Linear guide

• Roller guide

• Bushing

• Guided cylinder

38.7 Select Sensors and Control Method

• End-position sensors

• Encoder

• Linear scale

• PLC

• Motion controller

39. Mechanism Selection Criteria

The following factors should be evaluated when selecting a Mechanism.

39.1 Output Motion

• Linear

• Rotational

• Reciprocating

• Oscillating

• Intermittent

• Compound trajectory

39.2 Movement Range

• Travel distance

• Rotational angle

• Working range

• Space limitations

39.3 Speed Conditions

• Maximum speed

• Average speed

• Acceleration

• Deceleration

• Repetition period

39.4 Load Conditions

• Required force

• Required torque

• Mass

• Inertia

• Moment load

• Impact load

39.5 Accuracy Conditions

• Positioning accuracy

• Repeatability

• Path accuracy

• Backlash

• Settling time

39.6 Environmental Conditions

• Water and cleaning agents

• Dust

• High and low temperatures

• Corrosion

• Food contact

• Hygiene requirements

39.7 Maintenance Conditions

• Lubrication

• Wear

• Seal replacement

• Tension adjustment

• Cleaning access

• Component replaceability

40. Verification of Mechanism and Motion Design

40.1 Kinematic Verification

• Can the target position be reached?

• Is the required trajectory generated?

• Is the movement range sufficient?

• Is there interference between links?

• Are there singularities?

40.2 Velocity and Acceleration Verification

• Maximum speed

• Output-speed variation

• Acceleration

• Jerk

• Impact during direction reversal

40.3 Force and Torque Verification

• Actuator torque

• Output force

• Friction force

• Inertial force

• Bearing reaction force

• Link load

40.4 Structural Verification

• Stress

• Deformation

• Buckling

• Torsion

• Fatigue

• Resonance

40.5 Accuracy Verification

• Backlash

• Assembly tolerance

• Thermal deformation

• Repeatability

• Settling time

• Following error

40.6 Service-Life Verification

• Bearing life

• Guide life

• Ball-screw life

• Gear life

• Belt fatigue

• Chain wear

• Cam-contact fatigue

• Link-pin wear

41. Major Causes of Failure and Performance Degradation

Improper connection between Mechanism and Motion may cause the following problems.

41.1 Insufficient Actuator Capacity

• Failure to reach target speed

• Overheating

• Position error

• Step loss in stepper motors

• Servo overload

41.2 Insufficient Guide Capacity

• Table tilting

• Increased friction

• Localized wear

• Reduced repeatability

• Jamming

41.3 Increased Backlash

• Direction-reversal error

• Impact

• Noise

• Reduced positioning repeatability

41.4 Insufficient Rigidity

• Output deformation

• Vibration

• Increased settling time

• Machining error

41.5 Misalignment

• Bearing overload

• Coupling damage

• Ball-screw wear

• Seal damage

• Increased driving torque

41.6 Insufficient Lubrication

• Increased friction

• Heat generation

• Wear

• Noise

• Reduced service life

42. Connection Structure from a Safety Perspective

Mechanism and Motion design must analyze not only functional motion but also the flow of hazardous energy.

42.1 Main Hazards

• Pinching

• Cutting

• Collision

• Entanglement

• Falling

• Unexpected return

• Residual pressure

• Release of spring energy

• Residual motion caused by inertia

42.2 Safety Connection Structure

Safety sensor → Safety controller → Drive-energy isolation → Brake or stopping mechanism

42.3 Mechanical Safety Elements

• Stopper

• Brake

• Locking pin

• Torque limiter

• Slip clutch

• Fall-prevention device

• Overload-release device

• Safety cover

In an emergency stop, cutting motor power alone may not be sufficient. Vertical axes, large rotating bodies, springs, and hydraulic systems may require separate mechanical energy-control measures.

43. Connection Structure in Food-Processing Machinery

In food-processing machinery, hygiene and cleanability must be considered in addition to general motion performance.

Main Considerations

• Structure that prevents food residue accumulation

• Open frames and accessible guides

• Bearings and motors resistant to washdown

• Prevention of lubricant contact with food

• Cleanability of belts and chains

• Prevention of contamination at linkage joints

• Sealing structure

• Drainage structure

• Prevention of pneumatic exhaust contacting the product

In food-contact areas, direct-drive or enclosed-drive structures that are easy to clean may be more suitable than complex exposed linkages or screw mechanisms.

44. Summary of the Connection Structure Between Mechanism and Motion

The overall relationship between Mechanism and Motion can be summarized as follows.

Functional Connection

Required function → Required work → Required Motion → Suitable Mechanism

Energy Connection

Energy source → Actuator → Force or torque

Motion Connection

Input Motion → Transmission → Conversion → Constraint → Output Motion

Structural Connection

Frame → Bearings and guides → Links and shafts → Output element

Control Connection

Command → Controller → Drive → Actuator

Feedback Connection

Output Motion → Sensor → Controller → Correction

Work Connection

Output Motion → Tool → Product or process

45. Conclusion

The relationship between Mechanism and Motion cannot be explained simply by saying that a Mechanism creates movement.

An actuator converts energy into force and torque. The Mechanism transmits that force and torque while reorganizing the direction, distance, speed, trajectory, and magnitude of the output force.

Motion is the output of the Mechanism, but it is also an input condition for Mechanism design.

The designer must first define the required Motion and then select a Mechanism capable of generating it.

This process can be expressed as follows:

Functional requirements → Required Motion → Actuator selection → Mechanism selection → Guide-structure selection → Sensor and control configuration → Structural and life verification

A good Mechanism is not merely a structure that converts input motion into output motion.

It must satisfy the following conditions:

• It accurately generates the required trajectory.

• It achieves the required speed and acceleration.

• It transmits the necessary force and torque.

• It stably constrains unnecessary degrees of freedom.

• It limits backlash and deformation.

• It minimizes impact and vibration.

• It stops safely and maintains position.

• It provides sufficient life under repeated operation.

• It allows cleaning and maintenance.

• It connects reliably with the control system.

A Mechanism is the physical logic that forms Motion, while Motion is the way a machine performs its function.

Accurately defining the connection between these two elements is the starting point for determining the mechanical structure, drive system, control system, and overall equipment performance.