SSRAO

Explanation:
Lower pairs are those in which the two elements have surface (area) contact when relative motion takes place. Examples: sliding pair (prismatic), turning pair (revolute), screw pair, cylindrical pair, spherical pair, and planar pair. Higher pairs have point or line contact (e.g., cam-follower, gear teeth). The classification was introduced by Reuleaux.

Explanation:
Gruebler's (Kutzbach) criterion for planar mechanisms:
F = 3(n − 1) − 2j₁ − j₂
n = 8, j₁ = 10, j₂ = 0.
F = 3(8 − 1) − 2(10) = 21 − 20 = 1.
DOF = 1 means the mechanism is constrained — one input drives all other links.

Explanation:
Higher pairs have point or line contact between the two elements. A cam-and-follower pair has line (or point) contact and is the classic example of a higher pair. Sliding pair (prismatic), turning pair (revolute), and screw pair all have surface contact and are therefore lower pairs.

Explanation:
A screw pair allows only one degree of freedom — a combined rotation and translation linked by the lead of the screw. Although both rotation and translation occur simultaneously, they are not independent; specifying one completely determines the other. Hence DOF = 1. It is classified as a lower pair with surface contact.

Explanation:
Classification by DOF:
• F < 0 → Locked chain (over-constrained structure) — no relative motion possible.
• F = 0 → Statically determinate structure.
• F = 1 → Constrained mechanism (one input drives the system).
• F ≥ 2 → Unconstrained mechanism (needs multiple inputs).
A locked chain has F < 0, meaning it is over-constrained and behaves as a rigid structure.

Explanation:
The total number of instantaneous centres (I-centres) for a mechanism with n links:
N = n(n−1)/2
This is the combination C(n,2) — the number of ways to choose 2 links from n.
For a 4-bar linkage (n=4): N = 4×3/2 = 6 instantaneous centres.

Explanation:
Grashof's condition: s + l ≤ p + q.
s=20, l=60, p=40, q=50: 20+60=80 ≤ 40+50=90. ✓ Grashof satisfied.
Grashof's inversions:
• Shortest link fixed → Double-crank (drag-link) mechanism.
• Link adjacent to shortest fixed → Crank-rocker mechanism.
• Link opposite to shortest fixed → Double-rocker mechanism.
Fixing the shortest link (20 mm) gives a double-crank mechanism.

Explanation:
Grashof's condition: s + l ≤ p + q
where s = shortest link, l = longest link, p and q = the other two links.
If satisfied, at least one link can make a complete revolution (crank exists).
If s + l > p + q → non-Grashof linkage (all inversions are double-rockers).
If s + l = p + q → special change-point Grashof mechanism.

Explanation:
A spherical pair allows three independent rotations about three mutually perpendicular axes (roll, pitch, yaw). All translations are constrained. DOF = 3.
It is a lower pair (surface contact) and removes 3 DOF from the 6 DOF of a free body in space, constraining all three translations while allowing all three rotations.

Explanation:
The slider-crank chain has 4 links: crank, connecting rod, slider, and frame.
Inversions:
1st (frame fixed): Reciprocating engine / compressor.
2nd (crank fixed): Whitworth quick-return mechanism, Gnome engine.
3rd (connecting rod fixed): Oscillating cylinder engine.
4th (slider fixed): Hand pump.
The Whitworth quick-return mechanism is the 2nd inversion of the slider-crank chain.

Explanation:
A kinematic chain with 4 links and 4 turning (revolute) pairs is the four-bar chain. When one link is fixed (grounded), it becomes the four-bar mechanism — the most fundamental planar mechanism. DOF = 3(4−1)−2(4) = 1, confirming it is constrained.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁ − j₂
n = 6, j₁ = 7, j₂ = 0.
F = 3(6 − 1) − 2(7) = 15 − 14 = 1
DOF = 1 — constrained mechanism requiring one input to define all link positions.

Explanation:
A cylindrical pair allows two independent degrees of freedom:
1. Rotation about the common axis.
2. Translation along the same axis.
These two motions are independent (unlike a screw pair where they are coupled), giving DOF = 2. It is a lower pair with surface contact, removing 4 DOF from 6.

Explanation:
Lower pairs have surface (area) contact: turning pair, sliding pair, cylindrical pair, spherical pair, planar pair, and screw pair.
A gear pair has line contact (spur gears) or point contact (helical gears) between meshing teeth. Therefore, a gear pair is a higher pair, not a lower pair.

Explanation:
A constrained kinematic chain (mechanism) has exactly 1 DOF. This means that for a given input motion (one driving link), the positions of all other links are completely determined. DOF = 0 → structure. DOF ≥ 2 → unconstrained mechanism. DOF < 0 → super-structure (over-constrained).

Explanation:
The Ackermann steering mechanism is based on the four-bar chain. The four links are:
1. Front axle (fixed link / frame)
2. Left steering arm (crank)
3. Track rod (coupler)
4. Right steering arm (rocker)
It ensures the inner wheel turns through a larger angle than the outer wheel during cornering, satisfying the Ackermann condition for true rolling without lateral slip.

Explanation:
A planar pair allows three degrees of freedom:
1. Translation along the x-axis (in the plane).
2. Translation along the y-axis (in the plane).
3. Rotation about the z-axis (perpendicular to the plane).
It constrains only 3 DOF (translation perpendicular to the plane and two in-plane rotations), leaving DOF = 3. It is a lower pair with surface contact.

Explanation:
Kinematic pairs classified by closure:
• Closed (form-closed): Elements held together by geometry. Example: groove cam with follower (follower is constrained in a groove — cannot separate).
• Open (force-closed): Elements held together by external force (spring, gravity). Example: cam with spring-loaded follower.
Belt-pulley and chain-sprocket are wrapping pairs, not form-closed pairs.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁ − j₂
n = 5, j₁ = 5, j₂ = 0.
F = 3(5 − 1) − 2(5) = 12 − 10 = 2
DOF = 2 — unconstrained mechanism requiring two independent inputs.

Explanation:
The double slider-crank chain has 4 links: two sliding pairs and two turning pairs.
Inversions:
1st: Scotch-yoke mechanism.
2nd: Elliptical trammel.
3rd: Oldham's coupling (the link connecting the two sliders is fixed).
Oldham's coupling transmits rotation between two parallel but offset shafts with constant angular velocity ratio.

Explanation:
A turning pair (revolute pair) allows only one relative motion — rotation about a fixed axis. It constrains all translations (3) and two rotations, leaving only one rotational DOF. In a planar mechanism, a revolute joint removes 2 DOF from the 3 DOF of a free planar body, leaving 1 DOF. It is a lower pair with surface contact.

Explanation:
The elliptical trammel is the 2nd inversion of the double slider-crank chain. The two sliders move in perpendicular slots (fixed frame), and any point on the coupler traces an ellipse. The semi-axes of the ellipse equal the distances from the point to the two slider joints on the coupler. Used in engineering drawing instruments.

Explanation:
In the Whitworth quick-return mechanism, the time ratio is:
Time of cutting stroke / Time of return stroke = α / (360° − α)
where α is the angle subtended by the driving crank at the fixed pivot during the cutting (forward) stroke. Since α > 180°, the cutting stroke takes longer than the return stroke, making it a quick-return mechanism.

Explanation:
With 3 links and 3 turning pairs: F = 3(3−1) − 2(3) = 6 − 6 = 0 → structure.
With 4 links and 4 turning pairs: F = 3(4−1) − 2(4) = 9 − 8 = 1 → constrained mechanism.
Therefore, the minimum number of links for a kinematic chain (mechanism) with DOF=1 is 4.

Explanation:
Completely constrained motion: Motion is restricted to one definite direction by geometry alone, regardless of the applied force direction.
A square bar in a square hole can only slide (translate) — it cannot rotate. This is completely constrained motion.
A circular shaft in a circular hole can both rotate and slide — incompletely constrained.
A ball in a spherical socket has 3 rotational DOF — incompletely constrained.

Explanation:
The Scotch-yoke mechanism is the 1st inversion of the double slider-crank chain. A crank (pin) rotates and slides in a slotted yoke. The yoke translates in a fixed guide. If the crank rotates at uniform angular velocity ω, the displacement of the yoke is x = r·sin(ωt) — simple harmonic motion (SHM). Used in testing machines and hydraulic pumps requiring SHM.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁
n = 10, j₁ = 13.
F = 3(10 − 1) − 2(13) = 27 − 26 = 1
DOF = 1 — constrained mechanism. This is a common configuration for complex mechanisms like six-bar linkages with additional links.

Explanation:
A kinematic chain is an assembly of links connected by kinematic pairs such that relative motion between links is possible. It does NOT require a fixed link — that is the definition of a mechanism. When one link of a kinematic chain is fixed (grounded), it becomes a mechanism. A kinematic chain can have any DOF ≥ 1 and can include any type of kinematic pairs including sliding pairs.

Explanation:
Grashof's inversions (when Grashof condition s+l ≤ p+q is satisfied):
• Shortest link fixed → Double-crank (drag-link) mechanism.
• Link adjacent to shortest fixed → Crank-rocker mechanism.
• Link opposite to shortest fixed → Double-rocker mechanism.
When the link opposite to the shortest link is fixed, neither of the other two links can make a complete revolution — both oscillate, giving a double-rocker mechanism.

Explanation:
Kennedy's theorem (three-centre theorem): If three bodies have relative plane motion, their three instantaneous centres of relative motion must lie on a straight line (are collinear). This theorem is fundamental to the instantaneous centre method for velocity analysis of mechanisms. It allows unknown instantaneous centres to be located graphically using the known ones.

Explanation:
Number of instantaneous centres = n(n−1)/2
For n = 4 links: N = 4(4−1)/2 = 4×3/2 = 6
These 6 I-centres are: I₁₂, I₁₃, I₁₄, I₂₃, I₂₄, I₃₄.
Of these, 4 are primary (at the joints) and 2 are secondary (found using Kennedy's theorem).

Explanation:
The Geneva mechanism (Geneva wheel) converts continuous rotary motion of a driving wheel into intermittent rotary motion of the Geneva wheel. A pin on the driver engages slots in the Geneva wheel, causing it to rotate by 360°/n (n = number of slots) per revolution of the driver. Between engagements, the Geneva wheel is locked. Used in film projectors, indexing tables, and watches.

Explanation:
In a four-bar mechanism:
• Frame (fixed link): Stationary reference link.
• Crank: Connected to the frame; makes a complete revolution (360°).
• Rocker: Connected to the frame; oscillates (does not make full revolution).
• Coupler (connecting rod): Floating link connecting crank and rocker.
The crank is the input link that rotates continuously, driven by a motor or engine.

Explanation:
A free rigid body in 3-D space has 6 degrees of freedom:
• 3 translational DOF: along x, y, and z axes.
• 3 rotational DOF: about x (roll), y (pitch), and z (yaw) axes.
This is the basis for the Kutzbach criterion for spatial mechanisms:
F = 6(n−1) − 5j₁ − 4j₂ − 3j₃ − 2j₄ − j₅

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁ − j₂
Both revolute and sliding pairs are full joints (j₁), each removing 2 DOF.
n = 6, j₁ = 5 + 2 = 7, j₂ = 0.
F = 3(6 − 1) − 2(7) = 15 − 14 = 1
DOF = 1. Both revolute and prismatic (sliding) pairs are lower pairs with 1 DOF each, so they both count as full joints in Gruebler's formula.

Explanation:
A ball-and-socket joint (spherical pair):
• Contact type: Surface contact (ball surface contacts socket surface) → Lower pair.
• DOF: 3 rotational DOF (rotation about x, y, z axes); all translations constrained.
Therefore it is a lower pair with 3 DOF. It removes 3 DOF from the 6 DOF of a free body in space, constraining all three translations while allowing all three rotations.

Explanation:
For a Whitworth/crank-shaper quick-return mechanism:
Time ratio = α / (360° − α)
Given ratio = 2:1: α / (360° − α) = 2
α = 2(360° − α) = 720° − 2α
3α = 720° → α = 240°
The crank sweeps 240° during the cutting stroke and 120° during the return stroke, giving a 2:1 time ratio.

Explanation:
Inversions of the four-bar chain include:
• Beam engine (crank and lever mechanism)
• Coupling rod of a locomotive (double-crank mechanism)
• Watt's indicator mechanism (crank-rocker)
• Pantograph
The Whitworth quick-return mechanism is an inversion of the SINGLE SLIDER-CRANK chain (2nd inversion), NOT the four-bar chain. It involves a sliding pair, which is absent in the pure four-bar chain.

Explanation:
The coupling rod of a locomotive connects two wheels of equal diameter on the same axle. Both wheels (cranks) rotate continuously and in the same direction. This is a double-crank mechanism (parallel crank mechanism). It is an inversion of the four-bar chain where the shortest link is fixed, allowing both cranks to make complete revolutions.

Explanation:
A revolute pair (turning pair) allows only pure rotation about a fixed axis. All translations and other rotations are constrained. DOF = 1.
• Prismatic pair: pure translation only.
• Helical pair: coupled rotation and translation (1 DOF).
• Cylindrical pair: independent rotation AND translation (2 DOF).
The revolute pair is the most common joint in planar mechanisms.

Explanation:
When the Grashof condition is NOT satisfied (s + l > p + q), the linkage is a non-Grashof linkage. No link can make a complete revolution regardless of which link is fixed. All four inversions of a non-Grashof four-bar chain result in double-rocker mechanisms, where both input and output links only oscillate.

Explanation:
A free rigid body in 3-D space has 6 DOF. A revolute joint in 3-D space allows only 1 DOF (rotation about one axis). Therefore it removes 6 − 1 = 5 DOF.
This is why in the spatial Kutzbach criterion, revolute joints appear as j₁ with coefficient 5:
F = 6(n−1) − 5j₁ − 4j₂ − 3j₃ − 2j₄ − j₅

Explanation:
Watt's straight-line mechanism is a four-bar linkage designed so that a specific point on the coupler traces an approximate straight line over a portion of its path. James Watt developed this mechanism for the steam engine to guide the piston rod in a straight line. Other straight-line mechanisms include Roberts' mechanism, Chebyshev's mechanism, and Peaucellier's exact straight-line mechanism.

Explanation:
Links are classified by the number of pairs (joints) they form:
• Unary (singular) link: Connected to 1 other link.
• Binary link: Connected to 2 other links (has 2 joints).
• Ternary link: Connected to 3 other links (has 3 joints).
• Quaternary link: Connected to 4 other links (has 4 joints).
In a four-bar mechanism, all four links are binary links.

Explanation:
The Peaucellier-Lipkin mechanism (1864) was the first linkage capable of generating exact straight-line motion. It consists of 8 links (including the frame) and uses the principle of inversion in a circle. A point on the mechanism traces a perfectly straight line, unlike Watt's mechanism which only approximates a straight line. It was historically significant as it proved that exact straight-line motion could be generated by a linkage.

Explanation:
Using Gruebler's formula F = 3(n−1) − 2j:
• F > 0: Mechanism (unconstrained if F > 1, constrained if F = 1).
• F = 0: Statically determinate structure (no motion possible).
• F < 0: Over-constrained structure (locked chain / super-structure).
A mechanism is a 'locked structure' when F < 0 (over-constrained). F = 0 is a statically determinate structure with no motion.

Explanation:
Types of constrained motion:
• Completely constrained: Motion restricted to one direction by geometry alone (e.g., square bar in square hole — only slides).
• Incompletely constrained: Motion can occur in more than one direction (e.g., circular shaft in circular hole — can rotate or slide).
• Successfully constrained: Incompletely constrained motion made definite by an external force or additional element (e.g., circular shaft with a key — the key prevents rotation, leaving only sliding).
A circular shaft in a circular hole with a key is successfully constrained.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁
n = 9, j₁ = 11.
F = 3(9 − 1) − 2(11) = 3(8) − 22 = 24 − 22 = 2
DOF = 2 — unconstrained mechanism requiring two independent inputs to define the configuration of all links.

Explanation:
The Kutzbach criterion for spatial (3-D) mechanisms:
F = 6(n−1) − 5j₁ − 4j₂ − 3j₃ − 2j₄ − j₅
where:
• n = total number of links (including frame)
• j₁ = joints with 1 DOF (revolute, prismatic, screw) — remove 5 DOF each
• j₂ = joints with 2 DOF (cylindrical, universal) — remove 4 DOF each
• j₃ = joints with 3 DOF (spherical) — remove 3 DOF each
Option A is Gruebler's formula for planar mechanisms.

Explanation:
A constrained mechanism has exactly 1 degree of freedom. This means that for any given position of the driver (input link), the positions of all other links are uniquely determined. The motion of every follower is completely determined by the motion of the driver. This is the desired condition for most practical mechanisms like engines, compressors, and machine tools.

Explanation:
The Hart mechanism (1874) is a six-bar linkage that generates exact straight-line motion. It is simpler than the Peaucellier mechanism (8 links) as it uses only 6 links. Like the Peaucellier mechanism, it is based on the principle of inversion in a circle. Both are exact straight-line mechanisms, unlike Watt's, Roberts', and Chebyshev's mechanisms which only approximate straight-line motion.

Explanation:
The transmission angle (μ) in a four-bar mechanism is the angle between the coupler (connecting rod) and the rocker (output link). It measures the quality of force transmission from the coupler to the rocker.
• Ideal: μ = 90° (maximum force transmission).
• Acceptable range: 45° ≤ μ ≤ 135°.
• Poor transmission: μ close to 0° or 180° (mechanism may lock).

Explanation:
A sewing machine uses a slider-crank mechanism to convert the rotary motion of the hand wheel (crank) into the reciprocating (up-and-down) motion of the needle (slider). The crank rotates, the connecting rod (coupler) transmits motion, and the needle bar slides up and down in a guide. This is the 1st inversion of the slider-crank chain (frame fixed).

Explanation:
Wrapping pairs (flexible pairs) are kinematic pairs in which the two elements are connected by a flexible element such as a belt, rope, chain, or band. Examples:
• Belt and pulley
• Chain and sprocket
• Rope and drum
These are distinct from lower pairs (surface contact) and higher pairs (point/line contact). They can transmit motion and force but only in tension.

Explanation:
Link lengths: crank=20, coupler=50, rocker=40, frame=60.
s (shortest) = 20 mm (crank), l (longest) = 60 mm (frame), p=50, q=40.
Grashof check: s + l ≤ p + q → 20 + 60 = 80 ≤ 50 + 40 = 90 ✓
Grashof condition is satisfied. Since the shortest link (crank=20 mm) is adjacent to the fixed link (frame=60 mm), this is a crank-rocker mechanism — the crank makes a full revolution while the rocker oscillates.

Explanation:
Number of instantaneous centres = n(n−1)/2
For n = 6 links: N = 6(6−1)/2 = 6×5/2 = 15
Of these 15 I-centres:
• Primary (at joints): equal to the number of joints (e.g., 7 for a six-bar linkage).
• Secondary (found by Kennedy's theorem): 15 − 7 = 8.
All 15 must be located for complete velocity analysis using the I-centre method.

Explanation:
A kinematic link (element) is defined as a resistant body or a group of resistant bodies with no relative motion between them, which forms a single unit in a mechanism.
Key points:
• It must be resistant (rigid or semi-rigid) to transmit force.
• Parts with no relative motion between them are considered one link.
• A link can be a single rigid body or an assembly of parts (e.g., a connecting rod with its bolts and nuts is one link).
• Links can be binary, ternary, or quaternary based on the number of joints.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁
n = 12, j₁ = 16.
F = 3(12 − 1) − 2(16) = 3(11) − 32 = 33 − 32 = 1
DOF = 1 — constrained mechanism. Complex mechanisms with many links (like multi-bar linkages used in automotive suspensions) often have this configuration.

Explanation:
Dead-centre positions occur when the crank and coupler become collinear (aligned).
At these positions:
• The mechanism loses its ability to transmit motion (mechanical advantage → ∞ or 0).
• The transmission angle is either 0° or 180°.
• The mechanism cannot be driven from the output side through these positions.
There are two dead-centre positions per revolution:
1. Extended position: crank and coupler fully extended.
2. Folded position: crank and coupler fully folded (overlapping).
Flywheels are used to carry the mechanism through dead-centre positions.

Explanation:
Grashof's condition: s + l ≤ p + q
Link lengths: 30, 40, 60, 80 mm.
s (shortest) = 30 mm, l (longest) = 80 mm, p = 40 mm, q = 60 mm.
Check: s + l = 30 + 80 = 110 mm
p + q = 40 + 60 = 100 mm
110 > 100 → Grashof condition NOT satisfied.
This is a non-Grashof linkage. No link can make a complete revolution. All inversions result in double-rocker mechanisms.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁
n = 3, j₁ = 3.
F = 3(3 − 1) − 2(3) = 6 − 6 = 0
A three-link chain with three revolute joints forms a rigid triangle — a structure with no relative motion (F = 0). This is why the triangle is the most rigid structural shape and is used extensively in trusses and frames.

Explanation:
A pantograph is a four-bar linkage (parallelogram linkage) with specific proportional link lengths. A fixed pivot, a tracing point, and a drawing point are collinear with the fixed pivot. The ratio of distances determines the scale factor. When the tracing point follows a figure, the drawing point reproduces it at the scaled size. It exploits the property of similar triangles in the parallelogram linkage.

Explanation:
Inversions of the double slider-crank chain:
1st inversion: Scotch-yoke mechanism.
2nd inversion: Elliptical trammel.
3rd inversion: Oldham's coupling.
The Whitworth quick-return mechanism is an inversion of the SINGLE slider-crank chain (2nd inversion — crank fixed), NOT the double slider-crank chain. The double slider-crank chain has two sliding pairs and two turning pairs.

Explanation:
Kinematic pairs classified by closure:
• Closed (form-closed) pair: Elements held together by their geometry/shape. Example: nut and bolt, groove cam with follower.
• Open (force-closed) pair: Elements held in contact by external forces such as gravity, springs, or magnetic forces. Example: cam with spring-loaded follower, a ball resting in a socket under gravity.
Force-closed pairs can lose contact if the external force is removed.

Explanation:
Gruebler's formula: F = 3(n − 1) − 2j₁
n = 7, j₁ = 9.
F = 3(7 − 1) − 2(9) = 3(6) − 18 = 18 − 18 = 0
Hmm, F = 0 → structure. For F = 1 with n=7: 3(6)−2j=1 → j=8.5 (not integer).
With n=7, j=9: F=0. With n=7, j=8: F=2.
Correcting: n=7, j=9 gives F=0. The answer B=1 corresponds to n=7, j=8 or n=8, j=10.
For n=8, j=10: F=3(7)−2(10)=21−20=1. The question as stated (n=7, j=9) gives F=0.

Explanation:
Higher pairs have point or line contact between the two elements:
• Ball bearing: The rolling ball has point contact with the inner and outer races → higher pair.
• Cam and follower: Line or point contact → higher pair.
• Gear teeth: Line contact → higher pair.
Lower pairs (sliding, turning, screw) have surface contact. A ball bearing is a classic example of a higher pair used in practice.

Explanation:
The oscillating cylinder engine is the 3rd inversion of the single slider-crank chain (connecting rod fixed as the frame). In this inversion:
• The connecting rod is fixed.
• The cylinder (slider) oscillates about a fixed pivot.
• The crank rotates about the fixed end of the connecting rod.
This mechanism is used in some steam engines and hydraulic motors where the cylinder oscillates to accommodate the crank motion.

Explanation:
A turning pair (revolute pair) allows only rotation about a fixed axis between the two elements. The axis of rotation is fixed relative to both elements. Examples: a shaft in a bearing, a door hinge, a pin joint in a linkage. DOF = 1. It is a lower pair with surface contact and is the most common joint in planar mechanisms.

Explanation:
Grashof's condition: s + l ≤ p + q
Link lengths: 50, 60, 70, 80 mm.
s (shortest) = 50 mm, l (longest) = 80 mm, p = 60 mm, q = 70 mm.
Check: s + l = 50 + 80 = 130 mm
p + q = 60 + 70 = 130 mm
130 = 130 → s + l = p + q (change-point condition, not strictly satisfied as <).
This is a special Grashof linkage (change-point mechanism). For strict non-Grashof (s+l > p+q), all inversions are double-rockers. The change-point case is degenerate.

Explanation:
A reciprocating pump uses the slider-crank mechanism (1st inversion — frame fixed) to convert the rotary motion of the crank (driven by a motor) into the reciprocating (back-and-forth) motion of the piston (slider). The connecting rod (coupler) transmits motion from the crank to the piston. This is the same principle used in reciprocating engines, compressors, and hand pumps.