22-Mec-A2 Kinematics and Dynamics of Machines
Worked solutions to 13 past sittings (2013–2019), 85 questions. Pick a sitting, or start from a topic below.
- December 2019
- December 2018
- May 2018
- December 2017
- May 2017
- December 2016
- May 2016
- May 2015
- December 2014
- May 2014
- December 2013
- May 2013
- Undated paper
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Mechanical advantage (5 sittings): December 2018 Q1 · May 2017 Q1 · May 2015 Q1 · May 2014 Q1 · May 2013 Q1
- Mobility (5 sittings): December 2019 Q1 · December 2018 Q1 · May 2018 Q1 · May 2017 Q1 · Undated paper Q1
- Balancing (4 sittings): May 2018 Q5 · December 2017 Q5 · May 2017 Q4 · May 2016 Q4
- Instant centres (4 sittings): December 2017 Q1 · May 2015 Q1 · December 2014 Q1 · May 2014 Q1
- Output speed (4 sittings): May 2015 Q1 · December 2014 Q3 · May 2014 Q3 · Undated paper Q4
- Shaking force (4 sittings): December 2019 Q4 · December 2018 Q5 · May 2018 Q5 · December 2017 Q5
- Compound planetary gear reduction (3 sittings): May 2014 Q3 · December 2013 Q3 · May 2013 Q3
- Inverted crank-slider (3 sittings): May 2018 Q5 · December 2017 Q2 · December 2016 Q2
- Pressure angle (3 sittings): May 2018 Q3 · May 2014 Q2 · Undated paper Q3
- Radial cam (3 sittings): December 2016 Q4 · May 2015 Q2 · May 2013 Q2
- Radial cam with flat-faced follower (3 sittings): December 2017 Q3 · May 2017 Q2 · May 2016 Q2
- Six-bar mechanism (3 sittings): May 2015 Q1 · December 2014 Q1 · May 2014 Q1
- Two-stage planetary gear train (3 sittings): December 2018 Q4 · May 2017 Q3 · May 2016 Q3
- Accelerations (2 sittings): December 2014 Q2 · December 2013 Q1
- Compound planetary gear train (2 sittings): May 2015 Q3 · December 2014 Q3
Questions by sitting
December 2019
- Question 1: Mechanism analysis: link types & mobility, transmission angles & Grashof, and number synthesis
- Question 2: Mechanical advantage of a mechanical press
- Question 3: Velocity, image, Coriolis and sliding acceleration of an inverted crank‑slider
- Question 4: Shaking force and balancing of a 3‑cylinder single‑plane engine
- Question 5: Radial cam‑follower motion design (rise–dwell–fall)
- Question 6: Speed ratio of a compound epicyclic gear train
- Question 7: Simple pendulum striking a wall (impact & free vibration)
- Question 8: Spring design for a helicopter‑suspended patient bed (bounce & pitch)
December 2018
- Question 1: Number synthesis, mobility, mechanical advantage and kinematics
- Question 2: Velocity of link 6 by the graphical method
- Question 3: Cam–follower motion design
- Question 4: Two-stage planetary gear train
- Question 5: Shaking force and balancing of an inverted crank-slider
- Question 6: Plastic impact on a mass–spring–damper
- Question 7: Stiffening a beam–mass system with a spring
May 2018
- Question 1: Mobility, skeleton notation and Grashof analysis
- Question 2: Velocity analysis of a six-bar mechanism
- Question 3: Radial cam design — minimum-velocity fall and pressure angle
- Question 4: Compound planetary gear train with two ring brakes
- Question 5: Inverted crank-slider — kinematics, shaking force, balancing
- Question 6: Plastic impact into a mass–spring–damper (Part B)
- Question 7: Lateral vibration of a two-mass shaft (Part B)
December 2017
- Question 1: Six-bar punch mechanism — time ratio, instant centres, redesign
- Question 2: Inverted crank-slider — velocity analysis
- Question 3: Radial cam with flat-faced follower
- Question 4: Two-stage planetary gear train design
- Question 5: Inverted crank-slider — shaking force & balancing
- Question 6: Base-excited vibration of a mono-cycle model
- Question 7: Torsional vibration of a two-gear shaft
May 2017
- Question 1: Symmetric planar mechanism — redundancy, mobility, mechanical advantage
- Question 2: Radial cam with flat-faced follower — minimum-acceleration program
- Question 3: Two-stage planetary gear train — design for 1500→39 rpm
- Question 4: Four-bar shaking force and balancing
- Question 5: Base-excited quarter-car — steady-state amplitudes
- Question 6: Torsional vibration of a 3-rotor fixed–fixed shaft
December 2016
- Question 1: Three short mechanism questions
- Question 2: Inverted crank-slider — complete kinematic analysis
- Question 3: Shaking force of a two-cylinder opposed engine
- Question 4: Radial cam — minimum-peak-velocity rise
- Question 5: Two-stage planetary gear train with ring brakes
- Question 6: Double pendulum with a stopper (impact)
- Question 7: Lateral vibration of a power line (string)
May 2016
- Question 1: Mechanical advantage of an eight-bar mechanism
- Question 2: Radial cam with flat-faced follower — minimum-jerk motion design
- Question 3: Two-stage planetary gear train — planet count and speed ratios
- Question 4: Four-bar shaking force and balancing
- Question 5: Steady-state response to a wavy road (base excitation)
- Question 6: Inverted pendulum with a torsional spring
May 2015
- Question 1: Six-bar mechanism — instant centres, mechanical advantage & output speed
- Question 2: Radial cam — minimum-peak-acceleration design, flat-faced follower
- Question 3: Compound planetary gear train — arm speed & relative gear speed
- Question 4: Four-bar mechanism — shaking-force balancing to 50%
- Question 5: Coupled two-degree-of-freedom vibration
- Question 6: Pendulum with spring & damper, perfectly-plastic impact
December 2014
- Question 1: Six-bar mechanism — instant centres & output angular velocity
- Question 2: Four-bar function generator — output velocity & acceleration
- Question 3: Compound planetary gear train — output speed
- Question 4: 90° V-twin engine — primary shaking force
- Question 5: Spring–dashpot rigid-bar pendulum — damped free vibration
- Question 6: Three-degree-of-freedom system — modal analysis & forced response
May 2014
- Question 1: Six-bar mechanism — instant centres & mechanical advantage
- Question 2: Cycloidal radial cam — motion program, profile & pressure angle
- Question 3: Compound planetary gear reduction — output speed
- Question 4: Four-bar mechanism — shaking-force balancing
- Question 5: Plastic impact onto a spring–damper — free vibration
- Question 6: Two-DOF forced vibration — steady-state response
December 2013
- Question 1: Six-bar function generator — velocities & accelerations
- Question 2: Cycloidal radial cam design
- Question 3: Compound planetary gear reduction
- Question 4: Shaking-force balancing of a four-bar
- Question 5: Bead on a spinning ring — natural frequency
- Question 6: Steady-state response of a 2-DOF system
May 2013
- Question 1: Toggle Press — Mechanical Advantage
- Question 2: Radial Cam — 3-4-5 Polynomial Design
- Question 3: Compound Planetary Gear Reduction
- Question 4: 90° V-Twin — Primary Shaking Force
- Question 5: Rolling-Disk Impact & Damped Free Vibration
- Question 6: Torsional Vibration of a 3-Rotor Shaft
Undated paper
- Question 1: Mobility, synthesis and skeleton mechanisms
- Question 2: Graphical velocity analysis of a six-bar mechanism
- Question 3: High-speed radial cam — motion program and pressure angle
- Question 4: Planetary gear train — output speed and relative carrier speed
- Question 5: Shaking force of a four-bar crank-rocker and its balancing
- Question 6: Pendulum striking a wall — restitution and period
- Question 7: Two-DOF torsional vibration of a geared shaft